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parrot/lib/python3.10/site-packages/numpy/random/tests/data/sfc64_np126.pkl.gz

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parrot/lib/python3.10/site-packages/scipy/stats/_binned_statistic.py

@@ -0,0 +1,795 @@
+import builtins
+from warnings import catch_warnings, simplefilter
+import numpy as np
+from operator import index
+from collections import namedtuple
+
+__all__ = ['binned_statistic',
+           'binned_statistic_2d',
+           'binned_statistic_dd']
+
+
+BinnedStatisticResult = namedtuple('BinnedStatisticResult',
+                                   ('statistic', 'bin_edges', 'binnumber'))
+
+
+def binned_statistic(x, values, statistic='mean',
+                     bins=10, range=None):
+    """
+    Compute a binned statistic for one or more sets of data.
+
+    This is a generalization of a histogram function.  A histogram divides
+    the space into bins, and returns the count of the number of points in
+    each bin.  This function allows the computation of the sum, mean, median,
+    or other statistic of the values (or set of values) within each bin.
+
+    Parameters
+    ----------
+    x : (N,) array_like
+        A sequence of values to be binned.
+    values : (N,) array_like or list of (N,) array_like
+        The data on which the statistic will be computed.  This must be
+        the same shape as `x`, or a set of sequences - each the same shape as
+        `x`.  If `values` is a set of sequences, the statistic will be computed
+        on each independently.
+    statistic : string or callable, optional
+        The statistic to compute (default is 'mean').
+        The following statistics are available:
+
+          * 'mean' : compute the mean of values for points within each bin.
+            Empty bins will be represented by NaN.
+          * 'std' : compute the standard deviation within each bin. This
+            is implicitly calculated with ddof=0.
+          * 'median' : compute the median of values for points within each
+            bin. Empty bins will be represented by NaN.
+          * 'count' : compute the count of points within each bin.  This is
+            identical to an unweighted histogram.  `values` array is not
+            referenced.
+          * 'sum' : compute the sum of values for points within each bin.
+            This is identical to a weighted histogram.
+          * 'min' : compute the minimum of values for points within each bin.
+            Empty bins will be represented by NaN.
+          * 'max' : compute the maximum of values for point within each bin.
+            Empty bins will be represented by NaN.
+          * function : a user-defined function which takes a 1D array of
+            values, and outputs a single numerical statistic. This function
+            will be called on the values in each bin.  Empty bins will be
+            represented by function([]), or NaN if this returns an error.
+
+    bins : int or sequence of scalars, optional
+        If `bins` is an int, it defines the number of equal-width bins in the
+        given range (10 by default).  If `bins` is a sequence, it defines the
+        bin edges, including the rightmost edge, allowing for non-uniform bin
+        widths.  Values in `x` that are smaller than lowest bin edge are
+        assigned to bin number 0, values beyond the highest bin are assigned to
+        ``bins[-1]``.  If the bin edges are specified, the number of bins will
+        be, (nx = len(bins)-1).
+    range : (float, float) or [(float, float)], optional
+        The lower and upper range of the bins.  If not provided, range
+        is simply ``(x.min(), x.max())``.  Values outside the range are
+        ignored.
+
+    Returns
+    -------
+    statistic : array
+        The values of the selected statistic in each bin.
+    bin_edges : array of dtype float
+        Return the bin edges ``(length(statistic)+1)``.
+    binnumber: 1-D ndarray of ints
+        Indices of the bins (corresponding to `bin_edges`) in which each value
+        of `x` belongs.  Same length as `values`.  A binnumber of `i` means the
+        corresponding value is between (bin_edges[i-1], bin_edges[i]).
+
+    See Also
+    --------
+    numpy.digitize, numpy.histogram, binned_statistic_2d, binned_statistic_dd
+
+    Notes
+    -----
+    All but the last (righthand-most) bin is half-open.  In other words, if
+    `bins` is ``[1, 2, 3, 4]``, then the first bin is ``[1, 2)`` (including 1,
+    but excluding 2) and the second ``[2, 3)``.  The last bin, however, is
+    ``[3, 4]``, which *includes* 4.
+
+    .. versionadded:: 0.11.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+
+    First some basic examples:
+
+    Create two evenly spaced bins in the range of the given sample, and sum the
+    corresponding values in each of those bins:
+
+    >>> values = [1.0, 1.0, 2.0, 1.5, 3.0]
+    >>> stats.binned_statistic([1, 1, 2, 5, 7], values, 'sum', bins=2)
+    BinnedStatisticResult(statistic=array([4. , 4.5]),
+            bin_edges=array([1., 4., 7.]), binnumber=array([1, 1, 1, 2, 2]))
+
+    Multiple arrays of values can also be passed.  The statistic is calculated
+    on each set independently:
+
+    >>> values = [[1.0, 1.0, 2.0, 1.5, 3.0], [2.0, 2.0, 4.0, 3.0, 6.0]]
+    >>> stats.binned_statistic([1, 1, 2, 5, 7], values, 'sum', bins=2)
+    BinnedStatisticResult(statistic=array([[4. , 4.5],
+           [8. , 9. ]]), bin_edges=array([1., 4., 7.]),
+           binnumber=array([1, 1, 1, 2, 2]))
+
+    >>> stats.binned_statistic([1, 2, 1, 2, 4], np.arange(5), statistic='mean',
+    ...                        bins=3)
+    BinnedStatisticResult(statistic=array([1., 2., 4.]),
+            bin_edges=array([1., 2., 3., 4.]),
+            binnumber=array([1, 2, 1, 2, 3]))
+
+    As a second example, we now generate some random data of sailing boat speed
+    as a function of wind speed, and then determine how fast our boat is for
+    certain wind speeds:
+
+    >>> rng = np.random.default_rng()
+    >>> windspeed = 8 * rng.random(500)
+    >>> boatspeed = .3 * windspeed**.5 + .2 * rng.random(500)
+    >>> bin_means, bin_edges, binnumber = stats.binned_statistic(windspeed,
+    ...                 boatspeed, statistic='median', bins=[1,2,3,4,5,6,7])
+    >>> plt.figure()
+    >>> plt.plot(windspeed, boatspeed, 'b.', label='raw data')
+    >>> plt.hlines(bin_means, bin_edges[:-1], bin_edges[1:], colors='g', lw=5,
+    ...            label='binned statistic of data')
+    >>> plt.legend()
+
+    Now we can use ``binnumber`` to select all datapoints with a windspeed
+    below 1:
+
+    >>> low_boatspeed = boatspeed[binnumber == 0]
+
+    As a final example, we will use ``bin_edges`` and ``binnumber`` to make a
+    plot of a distribution that shows the mean and distribution around that
+    mean per bin, on top of a regular histogram and the probability
+    distribution function:
+
+    >>> x = np.linspace(0, 5, num=500)
+    >>> x_pdf = stats.maxwell.pdf(x)
+    >>> samples = stats.maxwell.rvs(size=10000)
+
+    >>> bin_means, bin_edges, binnumber = stats.binned_statistic(x, x_pdf,
+    ...         statistic='mean', bins=25)
+    >>> bin_width = (bin_edges[1] - bin_edges[0])
+    >>> bin_centers = bin_edges[1:] - bin_width/2
+
+    >>> plt.figure()
+    >>> plt.hist(samples, bins=50, density=True, histtype='stepfilled',
+    ...          alpha=0.2, label='histogram of data')
+    >>> plt.plot(x, x_pdf, 'r-', label='analytical pdf')
+    >>> plt.hlines(bin_means, bin_edges[:-1], bin_edges[1:], colors='g', lw=2,
+    ...            label='binned statistic of data')
+    >>> plt.plot((binnumber - 0.5) * bin_width, x_pdf, 'g.', alpha=0.5)
+    >>> plt.legend(fontsize=10)
+    >>> plt.show()
+
+    """
+    try:
+        N = len(bins)
+    except TypeError:
+        N = 1
+
+    if N != 1:
+        bins = [np.asarray(bins, float)]
+
+    if range is not None:
+        if len(range) == 2:
+            range = [range]
+
+    medians, edges, binnumbers = binned_statistic_dd(
+        [x], values, statistic, bins, range)
+
+    return BinnedStatisticResult(medians, edges[0], binnumbers)
+
+
+BinnedStatistic2dResult = namedtuple('BinnedStatistic2dResult',
+                                     ('statistic', 'x_edge', 'y_edge',
+                                      'binnumber'))
+
+
+def binned_statistic_2d(x, y, values, statistic='mean',
+                        bins=10, range=None, expand_binnumbers=False):
+    """
+    Compute a bidimensional binned statistic for one or more sets of data.
+
+    This is a generalization of a histogram2d function.  A histogram divides
+    the space into bins, and returns the count of the number of points in
+    each bin.  This function allows the computation of the sum, mean, median,
+    or other statistic of the values (or set of values) within each bin.
+
+    Parameters
+    ----------
+    x : (N,) array_like
+        A sequence of values to be binned along the first dimension.
+    y : (N,) array_like
+        A sequence of values to be binned along the second dimension.
+    values : (N,) array_like or list of (N,) array_like
+        The data on which the statistic will be computed.  This must be
+        the same shape as `x`, or a list of sequences - each with the same
+        shape as `x`.  If `values` is such a list, the statistic will be
+        computed on each independently.
+    statistic : string or callable, optional
+        The statistic to compute (default is 'mean').
+        The following statistics are available:
+
+          * 'mean' : compute the mean of values for points within each bin.
+            Empty bins will be represented by NaN.
+          * 'std' : compute the standard deviation within each bin. This
+            is implicitly calculated with ddof=0.
+          * 'median' : compute the median of values for points within each
+            bin. Empty bins will be represented by NaN.
+          * 'count' : compute the count of points within each bin.  This is
+            identical to an unweighted histogram.  `values` array is not
+            referenced.
+          * 'sum' : compute the sum of values for points within each bin.
+            This is identical to a weighted histogram.
+          * 'min' : compute the minimum of values for points within each bin.
+            Empty bins will be represented by NaN.
+          * 'max' : compute the maximum of values for point within each bin.
+            Empty bins will be represented by NaN.
+          * function : a user-defined function which takes a 1D array of
+            values, and outputs a single numerical statistic. This function
+            will be called on the values in each bin.  Empty bins will be
+            represented by function([]), or NaN if this returns an error.
+
+    bins : int or [int, int] or array_like or [array, array], optional
+        The bin specification:
+
+          * the number of bins for the two dimensions (nx = ny = bins),
+          * the number of bins in each dimension (nx, ny = bins),
+          * the bin edges for the two dimensions (x_edge = y_edge = bins),
+          * the bin edges in each dimension (x_edge, y_edge = bins).
+
+        If the bin edges are specified, the number of bins will be,
+        (nx = len(x_edge)-1, ny = len(y_edge)-1).
+
+    range : (2,2) array_like, optional
+        The leftmost and rightmost edges of the bins along each dimension
+        (if not specified explicitly in the `bins` parameters):
+        [[xmin, xmax], [ymin, ymax]]. All values outside of this range will be
+        considered outliers and not tallied in the histogram.
+    expand_binnumbers : bool, optional
+        'False' (default): the returned `binnumber` is a shape (N,) array of
+        linearized bin indices.
+        'True': the returned `binnumber` is 'unraveled' into a shape (2,N)
+        ndarray, where each row gives the bin numbers in the corresponding
+        dimension.
+        See the `binnumber` returned value, and the `Examples` section.
+
+        .. versionadded:: 0.17.0
+
+    Returns
+    -------
+    statistic : (nx, ny) ndarray
+        The values of the selected statistic in each two-dimensional bin.
+    x_edge : (nx + 1) ndarray
+        The bin edges along the first dimension.
+    y_edge : (ny + 1) ndarray
+        The bin edges along the second dimension.
+    binnumber : (N,) array of ints or (2,N) ndarray of ints
+        This assigns to each element of `sample` an integer that represents the
+        bin in which this observation falls.  The representation depends on the
+        `expand_binnumbers` argument.  See `Notes` for details.
+
+
+    See Also
+    --------
+    numpy.digitize, numpy.histogram2d, binned_statistic, binned_statistic_dd
+
+    Notes
+    -----
+    Binedges:
+    All but the last (righthand-most) bin is half-open.  In other words, if
+    `bins` is ``[1, 2, 3, 4]``, then the first bin is ``[1, 2)`` (including 1,
+    but excluding 2) and the second ``[2, 3)``.  The last bin, however, is
+    ``[3, 4]``, which *includes* 4.
+
+    `binnumber`:
+    This returned argument assigns to each element of `sample` an integer that
+    represents the bin in which it belongs.  The representation depends on the
+    `expand_binnumbers` argument. If 'False' (default): The returned
+    `binnumber` is a shape (N,) array of linearized indices mapping each
+    element of `sample` to its corresponding bin (using row-major ordering).
+    Note that the returned linearized bin indices are used for an array with
+    extra bins on the outer binedges to capture values outside of the defined
+    bin bounds.
+    If 'True': The returned `binnumber` is a shape (2,N) ndarray where
+    each row indicates bin placements for each dimension respectively.  In each
+    dimension, a binnumber of `i` means the corresponding value is between
+    (D_edge[i-1], D_edge[i]), where 'D' is either 'x' or 'y'.
+
+    .. versionadded:: 0.11.0
+
+    Examples
+    --------
+    >>> from scipy import stats
+
+    Calculate the counts with explicit bin-edges:
+
+    >>> x = [0.1, 0.1, 0.1, 0.6]
+    >>> y = [2.1, 2.6, 2.1, 2.1]
+    >>> binx = [0.0, 0.5, 1.0]
+    >>> biny = [2.0, 2.5, 3.0]
+    >>> ret = stats.binned_statistic_2d(x, y, None, 'count', bins=[binx, biny])
+    >>> ret.statistic
+    array([[2., 1.],
+           [1., 0.]])
+
+    The bin in which each sample is placed is given by the `binnumber`
+    returned parameter.  By default, these are the linearized bin indices:
+
+    >>> ret.binnumber
+    array([5, 6, 5, 9])
+
+    The bin indices can also be expanded into separate entries for each
+    dimension using the `expand_binnumbers` parameter:
+
+    >>> ret = stats.binned_statistic_2d(x, y, None, 'count', bins=[binx, biny],
+    ...                                 expand_binnumbers=True)
+    >>> ret.binnumber
+    array([[1, 1, 1, 2],
+           [1, 2, 1, 1]])
+
+    Which shows that the first three elements belong in the xbin 1, and the
+    fourth into xbin 2; and so on for y.
+
+    """
+
+    # This code is based on np.histogram2d
+    try:
+        N = len(bins)
+    except TypeError:
+        N = 1
+
+    if N != 1 and N != 2:
+        xedges = yedges = np.asarray(bins, float)
+        bins = [xedges, yedges]
+
+    medians, edges, binnumbers = binned_statistic_dd(
+        [x, y], values, statistic, bins, range,
+        expand_binnumbers=expand_binnumbers)
+
+    return BinnedStatistic2dResult(medians, edges[0], edges[1], binnumbers)
+
+
+BinnedStatisticddResult = namedtuple('BinnedStatisticddResult',
+                                     ('statistic', 'bin_edges',
+                                      'binnumber'))
+
+
+def _bincount(x, weights):
+    if np.iscomplexobj(weights):
+        a = np.bincount(x, np.real(weights))
+        b = np.bincount(x, np.imag(weights))
+        z = a + b*1j
+
+    else:
+        z = np.bincount(x, weights)
+    return z
+
+
+def binned_statistic_dd(sample, values, statistic='mean',
+                        bins=10, range=None, expand_binnumbers=False,
+                        binned_statistic_result=None):
+    """
+    Compute a multidimensional binned statistic for a set of data.
+
+    This is a generalization of a histogramdd function.  A histogram divides
+    the space into bins, and returns the count of the number of points in
+    each bin.  This function allows the computation of the sum, mean, median,
+    or other statistic of the values within each bin.
+
+    Parameters
+    ----------
+    sample : array_like
+        Data to histogram passed as a sequence of N arrays of length D, or
+        as an (N,D) array.
+    values : (N,) array_like or list of (N,) array_like
+        The data on which the statistic will be computed.  This must be
+        the same shape as `sample`, or a list of sequences - each with the
+        same shape as `sample`.  If `values` is such a list, the statistic
+        will be computed on each independently.
+    statistic : string or callable, optional
+        The statistic to compute (default is 'mean').
+        The following statistics are available:
+
+          * 'mean' : compute the mean of values for points within each bin.
+            Empty bins will be represented by NaN.
+          * 'median' : compute the median of values for points within each
+            bin. Empty bins will be represented by NaN.
+          * 'count' : compute the count of points within each bin.  This is
+            identical to an unweighted histogram.  `values` array is not
+            referenced.
+          * 'sum' : compute the sum of values for points within each bin.
+            This is identical to a weighted histogram.
+          * 'std' : compute the standard deviation within each bin. This
+            is implicitly calculated with ddof=0. If the number of values
+            within a given bin is 0 or 1, the computed standard deviation value
+            will be 0 for the bin.
+          * 'min' : compute the minimum of values for points within each bin.
+            Empty bins will be represented by NaN.
+          * 'max' : compute the maximum of values for point within each bin.
+            Empty bins will be represented by NaN.
+          * function : a user-defined function which takes a 1D array of
+            values, and outputs a single numerical statistic. This function
+            will be called on the values in each bin.  Empty bins will be
+            represented by function([]), or NaN if this returns an error.
+
+    bins : sequence or positive int, optional
+        The bin specification must be in one of the following forms:
+
+          * A sequence of arrays describing the bin edges along each dimension.
+          * The number of bins for each dimension (nx, ny, ... = bins).
+          * The number of bins for all dimensions (nx = ny = ... = bins).
+    range : sequence, optional
+        A sequence of lower and upper bin edges to be used if the edges are
+        not given explicitly in `bins`. Defaults to the minimum and maximum
+        values along each dimension.
+    expand_binnumbers : bool, optional
+        'False' (default): the returned `binnumber` is a shape (N,) array of
+        linearized bin indices.
+        'True': the returned `binnumber` is 'unraveled' into a shape (D,N)
+        ndarray, where each row gives the bin numbers in the corresponding
+        dimension.
+        See the `binnumber` returned value, and the `Examples` section of
+        `binned_statistic_2d`.
+    binned_statistic_result : binnedStatisticddResult
+        Result of a previous call to the function in order to reuse bin edges
+        and bin numbers with new values and/or a different statistic.
+        To reuse bin numbers, `expand_binnumbers` must have been set to False
+        (the default)
+
+        .. versionadded:: 0.17.0
+
+    Returns
+    -------
+    statistic : ndarray, shape(nx1, nx2, nx3,...)
+        The values of the selected statistic in each two-dimensional bin.
+    bin_edges : list of ndarrays
+        A list of D arrays describing the (nxi + 1) bin edges for each
+        dimension.
+    binnumber : (N,) array of ints or (D,N) ndarray of ints
+        This assigns to each element of `sample` an integer that represents the
+        bin in which this observation falls.  The representation depends on the
+        `expand_binnumbers` argument.  See `Notes` for details.
+
+
+    See Also
+    --------
+    numpy.digitize, numpy.histogramdd, binned_statistic, binned_statistic_2d
+
+    Notes
+    -----
+    Binedges:
+    All but the last (righthand-most) bin is half-open in each dimension.  In
+    other words, if `bins` is ``[1, 2, 3, 4]``, then the first bin is
+    ``[1, 2)`` (including 1, but excluding 2) and the second ``[2, 3)``.  The
+    last bin, however, is ``[3, 4]``, which *includes* 4.
+
+    `binnumber`:
+    This returned argument assigns to each element of `sample` an integer that
+    represents the bin in which it belongs.  The representation depends on the
+    `expand_binnumbers` argument. If 'False' (default): The returned
+    `binnumber` is a shape (N,) array of linearized indices mapping each
+    element of `sample` to its corresponding bin (using row-major ordering).
+    If 'True': The returned `binnumber` is a shape (D,N) ndarray where
+    each row indicates bin placements for each dimension respectively.  In each
+    dimension, a binnumber of `i` means the corresponding value is between
+    (bin_edges[D][i-1], bin_edges[D][i]), for each dimension 'D'.
+
+    .. versionadded:: 0.11.0
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import matplotlib.pyplot as plt
+    >>> from mpl_toolkits.mplot3d import Axes3D
+
+    Take an array of 600 (x, y) coordinates as an example.
+    `binned_statistic_dd` can handle arrays of higher dimension `D`. But a plot
+    of dimension `D+1` is required.
+
+    >>> mu = np.array([0., 1.])
+    >>> sigma = np.array([[1., -0.5],[-0.5, 1.5]])
+    >>> multinormal = stats.multivariate_normal(mu, sigma)
+    >>> data = multinormal.rvs(size=600, random_state=235412)
+    >>> data.shape
+    (600, 2)
+
+    Create bins and count how many arrays fall in each bin:
+
+    >>> N = 60
+    >>> x = np.linspace(-3, 3, N)
+    >>> y = np.linspace(-3, 4, N)
+    >>> ret = stats.binned_statistic_dd(data, np.arange(600), bins=[x, y],
+    ...                                 statistic='count')
+    >>> bincounts = ret.statistic
+
+    Set the volume and the location of bars:
+
+    >>> dx = x[1] - x[0]
+    >>> dy = y[1] - y[0]
+    >>> x, y = np.meshgrid(x[:-1]+dx/2, y[:-1]+dy/2)
+    >>> z = 0
+
+    >>> bincounts = bincounts.ravel()
+    >>> x = x.ravel()
+    >>> y = y.ravel()
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111, projection='3d')
+    >>> with np.errstate(divide='ignore'):   # silence random axes3d warning
+    ...     ax.bar3d(x, y, z, dx, dy, bincounts)
+
+    Reuse bin numbers and bin edges with new values:
+
+    >>> ret2 = stats.binned_statistic_dd(data, -np.arange(600),
+    ...                                  binned_statistic_result=ret,
+    ...                                  statistic='mean')
+    """
+    known_stats = ['mean', 'median', 'count', 'sum', 'std', 'min', 'max']
+    if not callable(statistic) and statistic not in known_stats:
+        raise ValueError(f'invalid statistic {statistic!r}')
+
+    try:
+        bins = index(bins)
+    except TypeError:
+        # bins is not an integer
+        pass
+    # If bins was an integer-like object, now it is an actual Python int.
+
+    # NOTE: for _bin_edges(), see e.g. gh-11365
+    if isinstance(bins, int) and not np.isfinite(sample).all():
+        raise ValueError(f'{sample!r} contains non-finite values.')
+
+    # `Ndim` is the number of dimensions (e.g. `2` for `binned_statistic_2d`)
+    # `Dlen` is the length of elements along each dimension.
+    # This code is based on np.histogramdd
+    try:
+        # `sample` is an ND-array.
+        Dlen, Ndim = sample.shape
+    except (AttributeError, ValueError):
+        # `sample` is a sequence of 1D arrays.
+        sample = np.atleast_2d(sample).T
+        Dlen, Ndim = sample.shape
+
+    # Store initial shape of `values` to preserve it in the output
+    values = np.asarray(values)
+    input_shape = list(values.shape)
+    # Make sure that `values` is 2D to iterate over rows
+    values = np.atleast_2d(values)
+    Vdim, Vlen = values.shape
+
+    # Make sure `values` match `sample`
+    if statistic != 'count' and Vlen != Dlen:
+        raise AttributeError('The number of `values` elements must match the '
+                             'length of each `sample` dimension.')
+
+    try:
+        M = len(bins)
+        if M != Ndim:
+            raise AttributeError('The dimension of bins must be equal '
+                                 'to the dimension of the sample x.')
+    except TypeError:
+        bins = Ndim * [bins]
+
+    if binned_statistic_result is None:
+        nbin, edges, dedges = _bin_edges(sample, bins, range)
+        binnumbers = _bin_numbers(sample, nbin, edges, dedges)
+    else:
+        edges = binned_statistic_result.bin_edges
+        nbin = np.array([len(edges[i]) + 1 for i in builtins.range(Ndim)])
+        # +1 for outlier bins
+        dedges = [np.diff(edges[i]) for i in builtins.range(Ndim)]
+        binnumbers = binned_statistic_result.binnumber
+
+    # Avoid overflow with double precision. Complex `values` -> `complex128`.
+    result_type = np.result_type(values, np.float64)
+    result = np.empty([Vdim, nbin.prod()], dtype=result_type)
+
+    if statistic in {'mean', np.mean}:
+        result.fill(np.nan)
+        flatcount = _bincount(binnumbers, None)
+        a = flatcount.nonzero()
+        for vv in builtins.range(Vdim):
+            flatsum = _bincount(binnumbers, values[vv])
+            result[vv, a] = flatsum[a] / flatcount[a]
+    elif statistic in {'std', np.std}:
+        result.fill(np.nan)
+        flatcount = _bincount(binnumbers, None)
+        a = flatcount.nonzero()
+        for vv in builtins.range(Vdim):
+            flatsum = _bincount(binnumbers, values[vv])
+            delta = values[vv] - flatsum[binnumbers] / flatcount[binnumbers]
+            std = np.sqrt(
+                _bincount(binnumbers, delta*np.conj(delta))[a] / flatcount[a]
+            )
+            result[vv, a] = std
+        result = np.real(result)
+    elif statistic == 'count':
+        result = np.empty([Vdim, nbin.prod()], dtype=np.float64)
+        result.fill(0)
+        flatcount = _bincount(binnumbers, None)
+        a = np.arange(len(flatcount))
+        result[:, a] = flatcount[np.newaxis, :]
+    elif statistic in {'sum', np.sum}:
+        result.fill(0)
+        for vv in builtins.range(Vdim):
+            flatsum = _bincount(binnumbers, values[vv])
+            a = np.arange(len(flatsum))
+            result[vv, a] = flatsum
+    elif statistic in {'median', np.median}:
+        result.fill(np.nan)
+        for vv in builtins.range(Vdim):
+            i = np.lexsort((values[vv], binnumbers))
+            _, j, counts = np.unique(binnumbers[i],
+                                     return_index=True, return_counts=True)
+            mid = j + (counts - 1) / 2
+            mid_a = values[vv, i][np.floor(mid).astype(int)]
+            mid_b = values[vv, i][np.ceil(mid).astype(int)]
+            medians = (mid_a + mid_b) / 2
+            result[vv, binnumbers[i][j]] = medians
+    elif statistic in {'min', np.min}:
+        result.fill(np.nan)
+        for vv in builtins.range(Vdim):
+            i = np.argsort(values[vv])[::-1]  # Reversed so the min is last
+            result[vv, binnumbers[i]] = values[vv, i]
+    elif statistic in {'max', np.max}:
+        result.fill(np.nan)
+        for vv in builtins.range(Vdim):
+            i = np.argsort(values[vv])
+            result[vv, binnumbers[i]] = values[vv, i]
+    elif callable(statistic):
+        with np.errstate(invalid='ignore'), catch_warnings():
+            simplefilter("ignore", RuntimeWarning)
+            try:
+                null = statistic([])
+            except Exception:
+                null = np.nan
+        if np.iscomplexobj(null):
+            result = result.astype(np.complex128)
+        result.fill(null)
+        try:
+            _calc_binned_statistic(
+                Vdim, binnumbers, result, values, statistic
+            )
+        except ValueError:
+            result = result.astype(np.complex128)
+            _calc_binned_statistic(
+                Vdim, binnumbers, result, values, statistic
+            )
+
+    # Shape into a proper matrix
+    result = result.reshape(np.append(Vdim, nbin))
+
+    # Remove outliers (indices 0 and -1 for each bin-dimension).
+    core = tuple([slice(None)] + Ndim * [slice(1, -1)])
+    result = result[core]
+
+    # Unravel binnumbers into an ndarray, each row the bins for each dimension
+    if expand_binnumbers and Ndim > 1:
+        binnumbers = np.asarray(np.unravel_index(binnumbers, nbin))
+
+    if np.any(result.shape[1:] != nbin - 2):
+        raise RuntimeError('Internal Shape Error')
+
+    # Reshape to have output (`result`) match input (`values`) shape
+    result = result.reshape(input_shape[:-1] + list(nbin-2))
+
+    return BinnedStatisticddResult(result, edges, binnumbers)
+
+
+def _calc_binned_statistic(Vdim, bin_numbers, result, values, stat_func):
+    unique_bin_numbers = np.unique(bin_numbers)
+    for vv in builtins.range(Vdim):
+        bin_map = _create_binned_data(bin_numbers, unique_bin_numbers,
+                                      values, vv)
+        for i in unique_bin_numbers:
+            stat = stat_func(np.array(bin_map[i]))
+            if np.iscomplexobj(stat) and not np.iscomplexobj(result):
+                raise ValueError("The statistic function returns complex ")
+            result[vv, i] = stat
+
+
+def _create_binned_data(bin_numbers, unique_bin_numbers, values, vv):
+    """ Create hashmap of bin ids to values in bins
+    key: bin number
+    value: list of binned data
+    """
+    bin_map = dict()
+    for i in unique_bin_numbers:
+        bin_map[i] = []
+    for i in builtins.range(len(bin_numbers)):
+        bin_map[bin_numbers[i]].append(values[vv, i])
+    return bin_map
+
+
+def _bin_edges(sample, bins=None, range=None):
+    """ Create edge arrays
+    """
+    Dlen, Ndim = sample.shape
+
+    nbin = np.empty(Ndim, int)    # Number of bins in each dimension
+    edges = Ndim * [None]         # Bin edges for each dim (will be 2D array)
+    dedges = Ndim * [None]        # Spacing between edges (will be 2D array)
+
+    # Select range for each dimension
+    # Used only if number of bins is given.
+    if range is None:
+        smin = np.atleast_1d(np.array(sample.min(axis=0), float))
+        smax = np.atleast_1d(np.array(sample.max(axis=0), float))
+    else:
+        if len(range) != Ndim:
+            raise ValueError(
+                f"range given for {len(range)} dimensions; {Ndim} required")
+        smin = np.empty(Ndim)
+        smax = np.empty(Ndim)
+        for i in builtins.range(Ndim):
+            if range[i][1] < range[i][0]:
+                raise ValueError(
+                    "In {}range, start must be <= stop".format(
+                        f"dimension {i + 1} of " if Ndim > 1 else ""))
+            smin[i], smax[i] = range[i]
+
+    # Make sure the bins have a finite width.
+    for i in builtins.range(len(smin)):
+        if smin[i] == smax[i]:
+            smin[i] = smin[i] - .5
+            smax[i] = smax[i] + .5
+
+    # Preserve sample floating point precision in bin edges
+    edges_dtype = (sample.dtype if np.issubdtype(sample.dtype, np.floating)
+                   else float)
+
+    # Create edge arrays
+    for i in builtins.range(Ndim):
+        if np.isscalar(bins[i]):
+            nbin[i] = bins[i] + 2  # +2 for outlier bins
+            edges[i] = np.linspace(smin[i], smax[i], nbin[i] - 1,
+                                   dtype=edges_dtype)
+        else:
+            edges[i] = np.asarray(bins[i], edges_dtype)
+            nbin[i] = len(edges[i]) + 1  # +1 for outlier bins
+        dedges[i] = np.diff(edges[i])
+
+    nbin = np.asarray(nbin)
+
+    return nbin, edges, dedges
+
+
+def _bin_numbers(sample, nbin, edges, dedges):
+    """Compute the bin number each sample falls into, in each dimension
+    """
+    Dlen, Ndim = sample.shape
+
+    sampBin = [
+        np.digitize(sample[:, i], edges[i])
+        for i in range(Ndim)
+    ]
+
+    # Using `digitize`, values that fall on an edge are put in the right bin.
+    # For the rightmost bin, we want values equal to the right
+    # edge to be counted in the last bin, and not as an outlier.
+    for i in range(Ndim):
+        # Find the rounding precision
+        dedges_min = dedges[i].min()
+        if dedges_min == 0:
+            raise ValueError('The smallest edge difference is numerically 0.')
+        decimal = int(-np.log10(dedges_min)) + 6
+        # Find which points are on the rightmost edge.
+        on_edge = np.where((sample[:, i] >= edges[i][-1]) &
+                           (np.around(sample[:, i], decimal) ==
+                            np.around(edges[i][-1], decimal)))[0]
+        # Shift these points one bin to the left.
+        sampBin[i][on_edge] -= 1
+
+    # Compute the sample indices in the flattened statistic matrix.
+    binnumbers = np.ravel_multi_index(sampBin, nbin)
+
+    return binnumbers

parrot/lib/python3.10/site-packages/scipy/stats/_common.py

@@ -0,0 +1,5 @@
+from collections import namedtuple
+
+
+ConfidenceInterval = namedtuple("ConfidenceInterval", ["low", "high"])
+ConfidenceInterval. __doc__ = "Class for confidence intervals."

parrot/lib/python3.10/site-packages/scipy/stats/_constants.py

@@ -0,0 +1,39 @@
+"""
+Statistics-related constants.
+
+"""
+import numpy as np
+
+
+# The smallest representable positive number such that 1.0 + _EPS != 1.0.
+_EPS = np.finfo(float).eps
+
+# The largest [in magnitude] usable floating value.
+_XMAX = np.finfo(float).max
+
+# The log of the largest usable floating value; useful for knowing
+# when exp(something) will overflow
+_LOGXMAX = np.log(_XMAX)
+
+# The smallest [in magnitude] usable (i.e. not subnormal) double precision
+# floating value.
+_XMIN = np.finfo(float).tiny
+
+# The log of the smallest [in magnitude] usable (i.e not subnormal)
+# double precision floating value.
+_LOGXMIN = np.log(_XMIN)
+
+# -special.psi(1)
+_EULER = 0.577215664901532860606512090082402431042
+
+# special.zeta(3, 1)  Apery's constant
+_ZETA3 = 1.202056903159594285399738161511449990765
+
+# sqrt(pi)
+_SQRT_PI = 1.772453850905516027298167483341145182798
+
+# sqrt(2/pi)
+_SQRT_2_OVER_PI = 0.7978845608028654
+
+# log(sqrt(2/pi))
+_LOG_SQRT_2_OVER_PI = -0.22579135264472744

parrot/lib/python3.10/site-packages/scipy/stats/_covariance.py

@@ -0,0 +1,633 @@
+from functools import cached_property
+
+import numpy as np
+from scipy import linalg
+from scipy.stats import _multivariate
+
+
+__all__ = ["Covariance"]
+
+
+class Covariance:
+    """
+    Representation of a covariance matrix
+
+    Calculations involving covariance matrices (e.g. data whitening,
+    multivariate normal function evaluation) are often performed more
+    efficiently using a decomposition of the covariance matrix instead of the
+    covariance matrix itself. This class allows the user to construct an
+    object representing a covariance matrix using any of several
+    decompositions and perform calculations using a common interface.
+
+    .. note::
+
+        The `Covariance` class cannot be instantiated directly. Instead, use
+        one of the factory methods (e.g. `Covariance.from_diagonal`).
+
+    Examples
+    --------
+    The `Covariance` class is used by calling one of its
+    factory methods to create a `Covariance` object, then pass that
+    representation of the `Covariance` matrix as a shape parameter of a
+    multivariate distribution.
+
+    For instance, the multivariate normal distribution can accept an array
+    representing a covariance matrix:
+
+    >>> from scipy import stats
+    >>> import numpy as np
+    >>> d = [1, 2, 3]
+    >>> A = np.diag(d)  # a diagonal covariance matrix
+    >>> x = [4, -2, 5]  # a point of interest
+    >>> dist = stats.multivariate_normal(mean=[0, 0, 0], cov=A)
+    >>> dist.pdf(x)
+    4.9595685102808205e-08
+
+    but the calculations are performed in a very generic way that does not
+    take advantage of any special properties of the covariance matrix. Because
+    our covariance matrix is diagonal, we can use ``Covariance.from_diagonal``
+    to create an object representing the covariance matrix, and
+    `multivariate_normal` can use this to compute the probability density
+    function more efficiently.
+
+    >>> cov = stats.Covariance.from_diagonal(d)
+    >>> dist = stats.multivariate_normal(mean=[0, 0, 0], cov=cov)
+    >>> dist.pdf(x)
+    4.9595685102808205e-08
+
+    """
+    def __init__(self):
+        message = ("The `Covariance` class cannot be instantiated directly. "
+                   "Please use one of the factory methods "
+                   "(e.g. `Covariance.from_diagonal`).")
+        raise NotImplementedError(message)
+
+    @staticmethod
+    def from_diagonal(diagonal):
+        r"""
+        Return a representation of a covariance matrix from its diagonal.
+
+        Parameters
+        ----------
+        diagonal : array_like
+            The diagonal elements of a diagonal matrix.
+
+        Notes
+        -----
+        Let the diagonal elements of a diagonal covariance matrix :math:`D` be
+        stored in the vector :math:`d`.
+
+        When all elements of :math:`d` are strictly positive, whitening of a
+        data point :math:`x` is performed by computing
+        :math:`x \cdot d^{-1/2}`, where the inverse square root can be taken
+        element-wise.
+        :math:`\log\det{D}` is calculated as :math:`-2 \sum(\log{d})`,
+        where the :math:`\log` operation is performed element-wise.
+
+        This `Covariance` class supports singular covariance matrices. When
+        computing ``_log_pdet``, non-positive elements of :math:`d` are
+        ignored. Whitening is not well defined when the point to be whitened
+        does not lie in the span of the columns of the covariance matrix. The
+        convention taken here is to treat the inverse square root of
+        non-positive elements of :math:`d` as zeros.
+
+        Examples
+        --------
+        Prepare a symmetric positive definite covariance matrix ``A`` and a
+        data point ``x``.
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> rng = np.random.default_rng()
+        >>> n = 5
+        >>> A = np.diag(rng.random(n))
+        >>> x = rng.random(size=n)
+
+        Extract the diagonal from ``A`` and create the `Covariance` object.
+
+        >>> d = np.diag(A)
+        >>> cov = stats.Covariance.from_diagonal(d)
+
+        Compare the functionality of the `Covariance` object against a
+        reference implementations.
+
+        >>> res = cov.whiten(x)
+        >>> ref = np.diag(d**-0.5) @ x
+        >>> np.allclose(res, ref)
+        True
+        >>> res = cov.log_pdet
+        >>> ref = np.linalg.slogdet(A)[-1]
+        >>> np.allclose(res, ref)
+        True
+
+        """
+        return CovViaDiagonal(diagonal)
+
+    @staticmethod
+    def from_precision(precision, covariance=None):
+        r"""
+        Return a representation of a covariance from its precision matrix.
+
+        Parameters
+        ----------
+        precision : array_like
+            The precision matrix; that is, the inverse of a square, symmetric,
+            positive definite covariance matrix.
+        covariance : array_like, optional
+            The square, symmetric, positive definite covariance matrix. If not
+            provided, this may need to be calculated (e.g. to evaluate the
+            cumulative distribution function of
+            `scipy.stats.multivariate_normal`) by inverting `precision`.
+
+        Notes
+        -----
+        Let the covariance matrix be :math:`A`, its precision matrix be
+        :math:`P = A^{-1}`, and :math:`L` be the lower Cholesky factor such
+        that :math:`L L^T = P`.
+        Whitening of a data point :math:`x` is performed by computing
+        :math:`x^T L`. :math:`\log\det{A}` is calculated as
+        :math:`-2tr(\log{L})`, where the :math:`\log` operation is performed
+        element-wise.
+
+        This `Covariance` class does not support singular covariance matrices
+        because the precision matrix does not exist for a singular covariance
+        matrix.
+
+        Examples
+        --------
+        Prepare a symmetric positive definite precision matrix ``P`` and a
+        data point ``x``. (If the precision matrix is not already available,
+        consider the other factory methods of the `Covariance` class.)
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> rng = np.random.default_rng()
+        >>> n = 5
+        >>> P = rng.random(size=(n, n))
+        >>> P = P @ P.T  # a precision matrix must be positive definite
+        >>> x = rng.random(size=n)
+
+        Create the `Covariance` object.
+
+        >>> cov = stats.Covariance.from_precision(P)
+
+        Compare the functionality of the `Covariance` object against
+        reference implementations.
+
+        >>> res = cov.whiten(x)
+        >>> ref = x @ np.linalg.cholesky(P)
+        >>> np.allclose(res, ref)
+        True
+        >>> res = cov.log_pdet
+        >>> ref = -np.linalg.slogdet(P)[-1]
+        >>> np.allclose(res, ref)
+        True
+
+        """
+        return CovViaPrecision(precision, covariance)
+
+    @staticmethod
+    def from_cholesky(cholesky):
+        r"""
+        Representation of a covariance provided via the (lower) Cholesky factor
+
+        Parameters
+        ----------
+        cholesky : array_like
+            The lower triangular Cholesky factor of the covariance matrix.
+
+        Notes
+        -----
+        Let the covariance matrix be :math:`A` and :math:`L` be the lower
+        Cholesky factor such that :math:`L L^T = A`.
+        Whitening of a data point :math:`x` is performed by computing
+        :math:`L^{-1} x`. :math:`\log\det{A}` is calculated as
+        :math:`2tr(\log{L})`, where the :math:`\log` operation is performed
+        element-wise.
+
+        This `Covariance` class does not support singular covariance matrices
+        because the Cholesky decomposition does not exist for a singular
+        covariance matrix.
+
+        Examples
+        --------
+        Prepare a symmetric positive definite covariance matrix ``A`` and a
+        data point ``x``.
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> rng = np.random.default_rng()
+        >>> n = 5
+        >>> A = rng.random(size=(n, n))
+        >>> A = A @ A.T  # make the covariance symmetric positive definite
+        >>> x = rng.random(size=n)
+
+        Perform the Cholesky decomposition of ``A`` and create the
+        `Covariance` object.
+
+        >>> L = np.linalg.cholesky(A)
+        >>> cov = stats.Covariance.from_cholesky(L)
+
+        Compare the functionality of the `Covariance` object against
+        reference implementation.
+
+        >>> from scipy.linalg import solve_triangular
+        >>> res = cov.whiten(x)
+        >>> ref = solve_triangular(L, x, lower=True)
+        >>> np.allclose(res, ref)
+        True
+        >>> res = cov.log_pdet
+        >>> ref = np.linalg.slogdet(A)[-1]
+        >>> np.allclose(res, ref)
+        True
+
+        """
+        return CovViaCholesky(cholesky)
+
+    @staticmethod
+    def from_eigendecomposition(eigendecomposition):
+        r"""
+        Representation of a covariance provided via eigendecomposition
+
+        Parameters
+        ----------
+        eigendecomposition : sequence
+            A sequence (nominally a tuple) containing the eigenvalue and
+            eigenvector arrays as computed by `scipy.linalg.eigh` or
+            `numpy.linalg.eigh`.
+
+        Notes
+        -----
+        Let the covariance matrix be :math:`A`, let :math:`V` be matrix of
+        eigenvectors, and let :math:`W` be the diagonal matrix of eigenvalues
+        such that `V W V^T = A`.
+
+        When all of the eigenvalues are strictly positive, whitening of a
+        data point :math:`x` is performed by computing
+        :math:`x^T (V W^{-1/2})`, where the inverse square root can be taken
+        element-wise.
+        :math:`\log\det{A}` is calculated as  :math:`tr(\log{W})`,
+        where the :math:`\log` operation is performed element-wise.
+
+        This `Covariance` class supports singular covariance matrices. When
+        computing ``_log_pdet``, non-positive eigenvalues are ignored.
+        Whitening is not well defined when the point to be whitened
+        does not lie in the span of the columns of the covariance matrix. The
+        convention taken here is to treat the inverse square root of
+        non-positive eigenvalues as zeros.
+
+        Examples
+        --------
+        Prepare a symmetric positive definite covariance matrix ``A`` and a
+        data point ``x``.
+
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> rng = np.random.default_rng()
+        >>> n = 5
+        >>> A = rng.random(size=(n, n))
+        >>> A = A @ A.T  # make the covariance symmetric positive definite
+        >>> x = rng.random(size=n)
+
+        Perform the eigendecomposition of ``A`` and create the `Covariance`
+        object.
+
+        >>> w, v = np.linalg.eigh(A)
+        >>> cov = stats.Covariance.from_eigendecomposition((w, v))
+
+        Compare the functionality of the `Covariance` object against
+        reference implementations.
+
+        >>> res = cov.whiten(x)
+        >>> ref = x @ (v @ np.diag(w**-0.5))
+        >>> np.allclose(res, ref)
+        True
+        >>> res = cov.log_pdet
+        >>> ref = np.linalg.slogdet(A)[-1]
+        >>> np.allclose(res, ref)
+        True
+
+        """
+        return CovViaEigendecomposition(eigendecomposition)
+
+    def whiten(self, x):
+        """
+        Perform a whitening transformation on data.
+
+        "Whitening" ("white" as in "white noise", in which each frequency has
+        equal magnitude) transforms a set of random variables into a new set of
+        random variables with unit-diagonal covariance. When a whitening
+        transform is applied to a sample of points distributed according to
+        a multivariate normal distribution with zero mean, the covariance of
+        the transformed sample is approximately the identity matrix.
+
+        Parameters
+        ----------
+        x : array_like
+            An array of points. The last dimension must correspond with the
+            dimensionality of the space, i.e., the number of columns in the
+            covariance matrix.
+
+        Returns
+        -------
+        x_ : array_like
+            The transformed array of points.
+
+        References
+        ----------
+        .. [1] "Whitening Transformation". Wikipedia.
+               https://en.wikipedia.org/wiki/Whitening_transformation
+        .. [2] Novak, Lukas, and Miroslav Vorechovsky. "Generalization of
+               coloring linear transformation". Transactions of VSB 18.2
+               (2018): 31-35. :doi:`10.31490/tces-2018-0013`
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> rng = np.random.default_rng()
+        >>> n = 3
+        >>> A = rng.random(size=(n, n))
+        >>> cov_array = A @ A.T  # make matrix symmetric positive definite
+        >>> precision = np.linalg.inv(cov_array)
+        >>> cov_object = stats.Covariance.from_precision(precision)
+        >>> x = rng.multivariate_normal(np.zeros(n), cov_array, size=(10000))
+        >>> x_ = cov_object.whiten(x)
+        >>> np.cov(x_, rowvar=False)  # near-identity covariance
+        array([[0.97862122, 0.00893147, 0.02430451],
+               [0.00893147, 0.96719062, 0.02201312],
+               [0.02430451, 0.02201312, 0.99206881]])
+
+        """
+        return self._whiten(np.asarray(x))
+
+    def colorize(self, x):
+        """
+        Perform a colorizing transformation on data.
+
+        "Colorizing" ("color" as in "colored noise", in which different
+        frequencies may have different magnitudes) transforms a set of
+        uncorrelated random variables into a new set of random variables with
+        the desired covariance. When a coloring transform is applied to a
+        sample of points distributed according to a multivariate normal
+        distribution with identity covariance and zero mean, the covariance of
+        the transformed sample is approximately the covariance matrix used
+        in the coloring transform.
+
+        Parameters
+        ----------
+        x : array_like
+            An array of points. The last dimension must correspond with the
+            dimensionality of the space, i.e., the number of columns in the
+            covariance matrix.
+
+        Returns
+        -------
+        x_ : array_like
+            The transformed array of points.
+
+        References
+        ----------
+        .. [1] "Whitening Transformation". Wikipedia.
+               https://en.wikipedia.org/wiki/Whitening_transformation
+        .. [2] Novak, Lukas, and Miroslav Vorechovsky. "Generalization of
+               coloring linear transformation". Transactions of VSB 18.2
+               (2018): 31-35. :doi:`10.31490/tces-2018-0013`
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> from scipy import stats
+        >>> rng = np.random.default_rng(1638083107694713882823079058616272161)
+        >>> n = 3
+        >>> A = rng.random(size=(n, n))
+        >>> cov_array = A @ A.T  # make matrix symmetric positive definite
+        >>> cholesky = np.linalg.cholesky(cov_array)
+        >>> cov_object = stats.Covariance.from_cholesky(cholesky)
+        >>> x = rng.multivariate_normal(np.zeros(n), np.eye(n), size=(10000))
+        >>> x_ = cov_object.colorize(x)
+        >>> cov_data = np.cov(x_, rowvar=False)
+        >>> np.allclose(cov_data, cov_array, rtol=3e-2)
+        True
+        """
+        return self._colorize(np.asarray(x))
+
+    @property
+    def log_pdet(self):
+        """
+        Log of the pseudo-determinant of the covariance matrix
+        """
+        return np.array(self._log_pdet, dtype=float)[()]
+
+    @property
+    def rank(self):
+        """
+        Rank of the covariance matrix
+        """
+        return np.array(self._rank, dtype=int)[()]
+
+    @property
+    def covariance(self):
+        """
+        Explicit representation of the covariance matrix
+        """
+        return self._covariance
+
+    @property
+    def shape(self):
+        """
+        Shape of the covariance array
+        """
+        return self._shape
+
+    def _validate_matrix(self, A, name):
+        A = np.atleast_2d(A)
+        m, n = A.shape[-2:]
+        if m != n or A.ndim != 2 or not (np.issubdtype(A.dtype, np.integer) or
+                                         np.issubdtype(A.dtype, np.floating)):
+            message = (f"The input `{name}` must be a square, "
+                       "two-dimensional array of real numbers.")
+            raise ValueError(message)
+        return A
+
+    def _validate_vector(self, A, name):
+        A = np.atleast_1d(A)
+        if A.ndim != 1 or not (np.issubdtype(A.dtype, np.integer) or
+                               np.issubdtype(A.dtype, np.floating)):
+            message = (f"The input `{name}` must be a one-dimensional array "
+                       "of real numbers.")
+            raise ValueError(message)
+        return A
+
+
+class CovViaPrecision(Covariance):
+
+    def __init__(self, precision, covariance=None):
+        precision = self._validate_matrix(precision, 'precision')
+        if covariance is not None:
+            covariance = self._validate_matrix(covariance, 'covariance')
+            message = "`precision.shape` must equal `covariance.shape`."
+            if precision.shape != covariance.shape:
+                raise ValueError(message)
+
+        self._chol_P = np.linalg.cholesky(precision)
+        self._log_pdet = -2*np.log(np.diag(self._chol_P)).sum(axis=-1)
+        self._rank = precision.shape[-1]  # must be full rank if invertible
+        self._precision = precision
+        self._cov_matrix = covariance
+        self._shape = precision.shape
+        self._allow_singular = False
+
+    def _whiten(self, x):
+        return x @ self._chol_P
+
+    @cached_property
+    def _covariance(self):
+        n = self._shape[-1]
+        return (linalg.cho_solve((self._chol_P, True), np.eye(n))
+                if self._cov_matrix is None else self._cov_matrix)
+
+    def _colorize(self, x):
+        return linalg.solve_triangular(self._chol_P.T, x.T, lower=False).T
+
+
+def _dot_diag(x, d):
+    # If d were a full diagonal matrix, x @ d would always do what we want.
+    # Special treatment is needed for n-dimensional `d` in which each row
+    # includes only the diagonal elements of a covariance matrix.
+    return x * d if x.ndim < 2 else x * np.expand_dims(d, -2)
+
+
+class CovViaDiagonal(Covariance):
+
+    def __init__(self, diagonal):
+        diagonal = self._validate_vector(diagonal, 'diagonal')
+
+        i_zero = diagonal <= 0
+        positive_diagonal = np.array(diagonal, dtype=np.float64)
+
+        positive_diagonal[i_zero] = 1  # ones don't affect determinant
+        self._log_pdet = np.sum(np.log(positive_diagonal), axis=-1)
+
+        psuedo_reciprocals = 1 / np.sqrt(positive_diagonal)
+        psuedo_reciprocals[i_zero] = 0
+
+        self._sqrt_diagonal = np.sqrt(diagonal)
+        self._LP = psuedo_reciprocals
+        self._rank = positive_diagonal.shape[-1] - i_zero.sum(axis=-1)
+        self._covariance = np.apply_along_axis(np.diag, -1, diagonal)
+        self._i_zero = i_zero
+        self._shape = self._covariance.shape
+        self._allow_singular = True
+
+    def _whiten(self, x):
+        return _dot_diag(x, self._LP)
+
+    def _colorize(self, x):
+        return _dot_diag(x, self._sqrt_diagonal)
+
+    def _support_mask(self, x):
+        """
+        Check whether x lies in the support of the distribution.
+        """
+        return ~np.any(_dot_diag(x, self._i_zero), axis=-1)
+
+
+class CovViaCholesky(Covariance):
+
+    def __init__(self, cholesky):
+        L = self._validate_matrix(cholesky, 'cholesky')
+
+        self._factor = L
+        self._log_pdet = 2*np.log(np.diag(self._factor)).sum(axis=-1)
+        self._rank = L.shape[-1]  # must be full rank for cholesky
+        self._shape = L.shape
+        self._allow_singular = False
+
+    @cached_property
+    def _covariance(self):
+        return self._factor @ self._factor.T
+
+    def _whiten(self, x):
+        res = linalg.solve_triangular(self._factor, x.T, lower=True).T
+        return res
+
+    def _colorize(self, x):
+        return x @ self._factor.T
+
+
+class CovViaEigendecomposition(Covariance):
+
+    def __init__(self, eigendecomposition):
+        eigenvalues, eigenvectors = eigendecomposition
+        eigenvalues = self._validate_vector(eigenvalues, 'eigenvalues')
+        eigenvectors = self._validate_matrix(eigenvectors, 'eigenvectors')
+        message = ("The shapes of `eigenvalues` and `eigenvectors` "
+                   "must be compatible.")
+        try:
+            eigenvalues = np.expand_dims(eigenvalues, -2)
+            eigenvectors, eigenvalues = np.broadcast_arrays(eigenvectors,
+                                                            eigenvalues)
+            eigenvalues = eigenvalues[..., 0, :]
+        except ValueError:
+            raise ValueError(message)
+
+        i_zero = eigenvalues <= 0
+        positive_eigenvalues = np.array(eigenvalues, dtype=np.float64)
+
+        positive_eigenvalues[i_zero] = 1  # ones don't affect determinant
+        self._log_pdet = np.sum(np.log(positive_eigenvalues), axis=-1)
+
+        psuedo_reciprocals = 1 / np.sqrt(positive_eigenvalues)
+        psuedo_reciprocals[i_zero] = 0
+
+        self._LP = eigenvectors * psuedo_reciprocals
+        self._LA = eigenvectors * np.sqrt(eigenvalues)
+        self._rank = positive_eigenvalues.shape[-1] - i_zero.sum(axis=-1)
+        self._w = eigenvalues
+        self._v = eigenvectors
+        self._shape = eigenvectors.shape
+        self._null_basis = eigenvectors * i_zero
+        # This is only used for `_support_mask`, not to decide whether
+        # the covariance is singular or not.
+        self._eps = _multivariate._eigvalsh_to_eps(eigenvalues) * 10**3
+        self._allow_singular = True
+
+    def _whiten(self, x):
+        return x @ self._LP
+
+    def _colorize(self, x):
+        return x @ self._LA.T
+
+    @cached_property
+    def _covariance(self):
+        return (self._v * self._w) @ self._v.T
+
+    def _support_mask(self, x):
+        """
+        Check whether x lies in the support of the distribution.
+        """
+        residual = np.linalg.norm(x @ self._null_basis, axis=-1)
+        in_support = residual < self._eps
+        return in_support
+
+
+class CovViaPSD(Covariance):
+    """
+    Representation of a covariance provided via an instance of _PSD
+    """
+
+    def __init__(self, psd):
+        self._LP = psd.U
+        self._log_pdet = psd.log_pdet
+        self._rank = psd.rank
+        self._covariance = psd._M
+        self._shape = psd._M.shape
+        self._psd = psd
+        self._allow_singular = False  # by default
+
+    def _whiten(self, x):
+        return x @ self._LP
+
+    def _support_mask(self, x):
+        return self._psd._support_mask(x)

parrot/lib/python3.10/site-packages/scipy/stats/_mgc.py

@@ -0,0 +1,550 @@
+import warnings
+import numpy as np
+
+from scipy._lib._util import check_random_state, MapWrapper, rng_integers, _contains_nan
+from scipy._lib._bunch import _make_tuple_bunch
+from scipy.spatial.distance import cdist
+from scipy.ndimage import _measurements
+
+from ._stats import _local_correlations  # type: ignore[import-not-found]
+from . import distributions
+
+__all__ = ['multiscale_graphcorr']
+
+# FROM MGCPY: https://github.com/neurodata/mgcpy
+
+
+class _ParallelP:
+    """Helper function to calculate parallel p-value."""
+
+    def __init__(self, x, y, random_states):
+        self.x = x
+        self.y = y
+        self.random_states = random_states
+
+    def __call__(self, index):
+        order = self.random_states[index].permutation(self.y.shape[0])
+        permy = self.y[order][:, order]
+
+        # calculate permuted stats, store in null distribution
+        perm_stat = _mgc_stat(self.x, permy)[0]
+
+        return perm_stat
+
+
+def _perm_test(x, y, stat, reps=1000, workers=-1, random_state=None):
+    r"""Helper function that calculates the p-value. See below for uses.
+
+    Parameters
+    ----------
+    x, y : ndarray
+        `x` and `y` have shapes `(n, p)` and `(n, q)`.
+    stat : float
+        The sample test statistic.
+    reps : int, optional
+        The number of replications used to estimate the null when using the
+        permutation test. The default is 1000 replications.
+    workers : int or map-like callable, optional
+        If `workers` is an int the population is subdivided into `workers`
+        sections and evaluated in parallel (uses
+        `multiprocessing.Pool <multiprocessing>`). Supply `-1` to use all cores
+        available to the Process. Alternatively supply a map-like callable,
+        such as `multiprocessing.Pool.map` for evaluating the population in
+        parallel. This evaluation is carried out as `workers(func, iterable)`.
+        Requires that `func` be pickleable.
+    random_state : {None, int, `numpy.random.Generator`,
+                    `numpy.random.RandomState`}, optional
+
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+
+    Returns
+    -------
+    pvalue : float
+        The sample test p-value.
+    null_dist : list
+        The approximated null distribution.
+
+    """
+    # generate seeds for each rep (change to new parallel random number
+    # capabilities in numpy >= 1.17+)
+    random_state = check_random_state(random_state)
+    random_states = [np.random.RandomState(rng_integers(random_state, 1 << 32,
+                     size=4, dtype=np.uint32)) for _ in range(reps)]
+
+    # parallelizes with specified workers over number of reps and set seeds
+    parallelp = _ParallelP(x=x, y=y, random_states=random_states)
+    with MapWrapper(workers) as mapwrapper:
+        null_dist = np.array(list(mapwrapper(parallelp, range(reps))))
+
+    # calculate p-value and significant permutation map through list
+    pvalue = (1 + (null_dist >= stat).sum()) / (1 + reps)
+
+    return pvalue, null_dist
+
+
+def _euclidean_dist(x):
+    return cdist(x, x)
+
+
+MGCResult = _make_tuple_bunch('MGCResult',
+                              ['statistic', 'pvalue', 'mgc_dict'], [])
+
+
+def multiscale_graphcorr(x, y, compute_distance=_euclidean_dist, reps=1000,
+                         workers=1, is_twosamp=False, random_state=None):
+    r"""Computes the Multiscale Graph Correlation (MGC) test statistic.
+
+    Specifically, for each point, MGC finds the :math:`k`-nearest neighbors for
+    one property (e.g. cloud density), and the :math:`l`-nearest neighbors for
+    the other property (e.g. grass wetness) [1]_. This pair :math:`(k, l)` is
+    called the "scale". A priori, however, it is not know which scales will be
+    most informative. So, MGC computes all distance pairs, and then efficiently
+    computes the distance correlations for all scales. The local correlations
+    illustrate which scales are relatively informative about the relationship.
+    The key, therefore, to successfully discover and decipher relationships
+    between disparate data modalities is to adaptively determine which scales
+    are the most informative, and the geometric implication for the most
+    informative scales. Doing so not only provides an estimate of whether the
+    modalities are related, but also provides insight into how the
+    determination was made. This is especially important in high-dimensional
+    data, where simple visualizations do not reveal relationships to the
+    unaided human eye. Characterizations of this implementation in particular
+    have been derived from and benchmarked within in [2]_.
+
+    Parameters
+    ----------
+    x, y : ndarray
+        If ``x`` and ``y`` have shapes ``(n, p)`` and ``(n, q)`` where `n` is
+        the number of samples and `p` and `q` are the number of dimensions,
+        then the MGC independence test will be run.  Alternatively, ``x`` and
+        ``y`` can have shapes ``(n, n)`` if they are distance or similarity
+        matrices, and ``compute_distance`` must be sent to ``None``. If ``x``
+        and ``y`` have shapes ``(n, p)`` and ``(m, p)``, an unpaired
+        two-sample MGC test will be run.
+    compute_distance : callable, optional
+        A function that computes the distance or similarity among the samples
+        within each data matrix. Set to ``None`` if ``x`` and ``y`` are
+        already distance matrices. The default uses the euclidean norm metric.
+        If you are calling a custom function, either create the distance
+        matrix before-hand or create a function of the form
+        ``compute_distance(x)`` where `x` is the data matrix for which
+        pairwise distances are calculated.
+    reps : int, optional
+        The number of replications used to estimate the null when using the
+        permutation test. The default is ``1000``.
+    workers : int or map-like callable, optional
+        If ``workers`` is an int the population is subdivided into ``workers``
+        sections and evaluated in parallel (uses ``multiprocessing.Pool
+        <multiprocessing>``). Supply ``-1`` to use all cores available to the
+        Process. Alternatively supply a map-like callable, such as
+        ``multiprocessing.Pool.map`` for evaluating the p-value in parallel.
+        This evaluation is carried out as ``workers(func, iterable)``.
+        Requires that `func` be pickleable. The default is ``1``.
+    is_twosamp : bool, optional
+        If `True`, a two sample test will be run. If ``x`` and ``y`` have
+        shapes ``(n, p)`` and ``(m, p)``, this optional will be overridden and
+        set to ``True``. Set to ``True`` if ``x`` and ``y`` both have shapes
+        ``(n, p)`` and a two sample test is desired. The default is ``False``.
+        Note that this will not run if inputs are distance matrices.
+    random_state : {None, int, `numpy.random.Generator`,
+                    `numpy.random.RandomState`}, optional
+
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+
+    Returns
+    -------
+    res : MGCResult
+        An object containing attributes:
+
+        statistic : float
+            The sample MGC test statistic within `[-1, 1]`.
+        pvalue : float
+            The p-value obtained via permutation.
+        mgc_dict : dict
+            Contains additional useful results:
+
+                - mgc_map : ndarray
+                    A 2D representation of the latent geometry of the
+                    relationship.
+                - opt_scale : (int, int)
+                    The estimated optimal scale as a `(x, y)` pair.
+                - null_dist : list
+                    The null distribution derived from the permuted matrices.
+
+    See Also
+    --------
+    pearsonr : Pearson correlation coefficient and p-value for testing
+               non-correlation.
+    kendalltau : Calculates Kendall's tau.
+    spearmanr : Calculates a Spearman rank-order correlation coefficient.
+
+    Notes
+    -----
+    A description of the process of MGC and applications on neuroscience data
+    can be found in [1]_. It is performed using the following steps:
+
+    #. Two distance matrices :math:`D^X` and :math:`D^Y` are computed and
+       modified to be mean zero columnwise. This results in two
+       :math:`n \times n` distance matrices :math:`A` and :math:`B` (the
+       centering and unbiased modification) [3]_.
+
+    #. For all values :math:`k` and :math:`l` from :math:`1, ..., n`,
+
+       * The :math:`k`-nearest neighbor and :math:`l`-nearest neighbor graphs
+         are calculated for each property. Here, :math:`G_k (i, j)` indicates
+         the :math:`k`-smallest values of the :math:`i`-th row of :math:`A`
+         and :math:`H_l (i, j)` indicates the :math:`l` smallested values of
+         the :math:`i`-th row of :math:`B`
+
+       * Let :math:`\circ` denotes the entry-wise matrix product, then local
+         correlations are summed and normalized using the following statistic:
+
+    .. math::
+
+        c^{kl} = \frac{\sum_{ij} A G_k B H_l}
+                      {\sqrt{\sum_{ij} A^2 G_k \times \sum_{ij} B^2 H_l}}
+
+    #. The MGC test statistic is the smoothed optimal local correlation of
+       :math:`\{ c^{kl} \}`. Denote the smoothing operation as :math:`R(\cdot)`
+       (which essentially set all isolated large correlations) as 0 and
+       connected large correlations the same as before, see [3]_.) MGC is,
+
+    .. math::
+
+        MGC_n (x, y) = \max_{(k, l)} R \left(c^{kl} \left( x_n, y_n \right)
+                                                    \right)
+
+    The test statistic returns a value between :math:`(-1, 1)` since it is
+    normalized.
+
+    The p-value returned is calculated using a permutation test. This process
+    is completed by first randomly permuting :math:`y` to estimate the null
+    distribution and then calculating the probability of observing a test
+    statistic, under the null, at least as extreme as the observed test
+    statistic.
+
+    MGC requires at least 5 samples to run with reliable results. It can also
+    handle high-dimensional data sets.
+    In addition, by manipulating the input data matrices, the two-sample
+    testing problem can be reduced to the independence testing problem [4]_.
+    Given sample data :math:`U` and :math:`V` of sizes :math:`p \times n`
+    :math:`p \times m`, data matrix :math:`X` and :math:`Y` can be created as
+    follows:
+
+    .. math::
+
+        X = [U | V] \in \mathcal{R}^{p \times (n + m)}
+        Y = [0_{1 \times n} | 1_{1 \times m}] \in \mathcal{R}^{(n + m)}
+
+    Then, the MGC statistic can be calculated as normal. This methodology can
+    be extended to similar tests such as distance correlation [4]_.
+
+    .. versionadded:: 1.4.0
+
+    References
+    ----------
+    .. [1] Vogelstein, J. T., Bridgeford, E. W., Wang, Q., Priebe, C. E.,
+           Maggioni, M., & Shen, C. (2019). Discovering and deciphering
+           relationships across disparate data modalities. ELife.
+    .. [2] Panda, S., Palaniappan, S., Xiong, J., Swaminathan, A.,
+           Ramachandran, S., Bridgeford, E. W., ... Vogelstein, J. T. (2019).
+           mgcpy: A Comprehensive High Dimensional Independence Testing Python
+           Package. :arXiv:`1907.02088`
+    .. [3] Shen, C., Priebe, C.E., & Vogelstein, J. T. (2019). From distance
+           correlation to multiscale graph correlation. Journal of the American
+           Statistical Association.
+    .. [4] Shen, C. & Vogelstein, J. T. (2018). The Exact Equivalence of
+           Distance and Kernel Methods for Hypothesis Testing.
+           :arXiv:`1806.05514`
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats import multiscale_graphcorr
+    >>> x = np.arange(100)
+    >>> y = x
+    >>> res = multiscale_graphcorr(x, y)
+    >>> res.statistic, res.pvalue
+    (1.0, 0.001)
+
+    To run an unpaired two-sample test,
+
+    >>> x = np.arange(100)
+    >>> y = np.arange(79)
+    >>> res = multiscale_graphcorr(x, y)
+    >>> res.statistic, res.pvalue  # doctest: +SKIP
+    (0.033258146255703246, 0.023)
+
+    or, if shape of the inputs are the same,
+
+    >>> x = np.arange(100)
+    >>> y = x
+    >>> res = multiscale_graphcorr(x, y, is_twosamp=True)
+    >>> res.statistic, res.pvalue  # doctest: +SKIP
+    (-0.008021809890200488, 1.0)
+
+    """
+    if not isinstance(x, np.ndarray) or not isinstance(y, np.ndarray):
+        raise ValueError("x and y must be ndarrays")
+
+    # convert arrays of type (n,) to (n, 1)
+    if x.ndim == 1:
+        x = x[:, np.newaxis]
+    elif x.ndim != 2:
+        raise ValueError(f"Expected a 2-D array `x`, found shape {x.shape}")
+    if y.ndim == 1:
+        y = y[:, np.newaxis]
+    elif y.ndim != 2:
+        raise ValueError(f"Expected a 2-D array `y`, found shape {y.shape}")
+
+    nx, px = x.shape
+    ny, py = y.shape
+
+    # check for NaNs
+    _contains_nan(x, nan_policy='raise')
+    _contains_nan(y, nan_policy='raise')
+
+    # check for positive or negative infinity and raise error
+    if np.sum(np.isinf(x)) > 0 or np.sum(np.isinf(y)) > 0:
+        raise ValueError("Inputs contain infinities")
+
+    if nx != ny:
+        if px == py:
+            # reshape x and y for two sample testing
+            is_twosamp = True
+        else:
+            raise ValueError("Shape mismatch, x and y must have shape [n, p] "
+                             "and [n, q] or have shape [n, p] and [m, p].")
+
+    if nx < 5 or ny < 5:
+        raise ValueError("MGC requires at least 5 samples to give reasonable "
+                         "results.")
+
+    # convert x and y to float
+    x = x.astype(np.float64)
+    y = y.astype(np.float64)
+
+    # check if compute_distance_matrix if a callable()
+    if not callable(compute_distance) and compute_distance is not None:
+        raise ValueError("Compute_distance must be a function.")
+
+    # check if number of reps exists, integer, or > 0 (if under 1000 raises
+    # warning)
+    if not isinstance(reps, int) or reps < 0:
+        raise ValueError("Number of reps must be an integer greater than 0.")
+    elif reps < 1000:
+        msg = ("The number of replications is low (under 1000), and p-value "
+               "calculations may be unreliable. Use the p-value result, with "
+               "caution!")
+        warnings.warn(msg, RuntimeWarning, stacklevel=2)
+
+    if is_twosamp:
+        if compute_distance is None:
+            raise ValueError("Cannot run if inputs are distance matrices")
+        x, y = _two_sample_transform(x, y)
+
+    if compute_distance is not None:
+        # compute distance matrices for x and y
+        x = compute_distance(x)
+        y = compute_distance(y)
+
+    # calculate MGC stat
+    stat, stat_dict = _mgc_stat(x, y)
+    stat_mgc_map = stat_dict["stat_mgc_map"]
+    opt_scale = stat_dict["opt_scale"]
+
+    # calculate permutation MGC p-value
+    pvalue, null_dist = _perm_test(x, y, stat, reps=reps, workers=workers,
+                                   random_state=random_state)
+
+    # save all stats (other than stat/p-value) in dictionary
+    mgc_dict = {"mgc_map": stat_mgc_map,
+                "opt_scale": opt_scale,
+                "null_dist": null_dist}
+
+    # create result object with alias for backward compatibility
+    res = MGCResult(stat, pvalue, mgc_dict)
+    res.stat = stat
+    return res
+
+
+def _mgc_stat(distx, disty):
+    r"""Helper function that calculates the MGC stat. See above for use.
+
+    Parameters
+    ----------
+    distx, disty : ndarray
+        `distx` and `disty` have shapes `(n, p)` and `(n, q)` or
+        `(n, n)` and `(n, n)`
+        if distance matrices.
+
+    Returns
+    -------
+    stat : float
+        The sample MGC test statistic within `[-1, 1]`.
+    stat_dict : dict
+        Contains additional useful additional returns containing the following
+        keys:
+
+            - stat_mgc_map : ndarray
+                MGC-map of the statistics.
+            - opt_scale : (float, float)
+                The estimated optimal scale as a `(x, y)` pair.
+
+    """
+    # calculate MGC map and optimal scale
+    stat_mgc_map = _local_correlations(distx, disty, global_corr='mgc')
+
+    n, m = stat_mgc_map.shape
+    if m == 1 or n == 1:
+        # the global scale at is the statistic calculated at maximial nearest
+        # neighbors. There is not enough local scale to search over, so
+        # default to global scale
+        stat = stat_mgc_map[m - 1][n - 1]
+        opt_scale = m * n
+    else:
+        samp_size = len(distx) - 1
+
+        # threshold to find connected region of significant local correlations
+        sig_connect = _threshold_mgc_map(stat_mgc_map, samp_size)
+
+        # maximum within the significant region
+        stat, opt_scale = _smooth_mgc_map(sig_connect, stat_mgc_map)
+
+    stat_dict = {"stat_mgc_map": stat_mgc_map,
+                 "opt_scale": opt_scale}
+
+    return stat, stat_dict
+
+
+def _threshold_mgc_map(stat_mgc_map, samp_size):
+    r"""
+    Finds a connected region of significance in the MGC-map by thresholding.
+
+    Parameters
+    ----------
+    stat_mgc_map : ndarray
+        All local correlations within `[-1,1]`.
+    samp_size : int
+        The sample size of original data.
+
+    Returns
+    -------
+    sig_connect : ndarray
+        A binary matrix with 1's indicating the significant region.
+
+    """
+    m, n = stat_mgc_map.shape
+
+    # 0.02 is simply an empirical threshold, this can be set to 0.01 or 0.05
+    # with varying levels of performance. Threshold is based on a beta
+    # approximation.
+    per_sig = 1 - (0.02 / samp_size)  # Percentile to consider as significant
+    threshold = samp_size * (samp_size - 3)/4 - 1/2  # Beta approximation
+    threshold = distributions.beta.ppf(per_sig, threshold, threshold) * 2 - 1
+
+    # the global scale at is the statistic calculated at maximial nearest
+    # neighbors. Threshold is the maximum on the global and local scales
+    threshold = max(threshold, stat_mgc_map[m - 1][n - 1])
+
+    # find the largest connected component of significant correlations
+    sig_connect = stat_mgc_map > threshold
+    if np.sum(sig_connect) > 0:
+        sig_connect, _ = _measurements.label(sig_connect)
+        _, label_counts = np.unique(sig_connect, return_counts=True)
+
+        # skip the first element in label_counts, as it is count(zeros)
+        max_label = np.argmax(label_counts[1:]) + 1
+        sig_connect = sig_connect == max_label
+    else:
+        sig_connect = np.array([[False]])
+
+    return sig_connect
+
+
+def _smooth_mgc_map(sig_connect, stat_mgc_map):
+    """Finds the smoothed maximal within the significant region R.
+
+    If area of R is too small it returns the last local correlation. Otherwise,
+    returns the maximum within significant_connected_region.
+
+    Parameters
+    ----------
+    sig_connect : ndarray
+        A binary matrix with 1's indicating the significant region.
+    stat_mgc_map : ndarray
+        All local correlations within `[-1, 1]`.
+
+    Returns
+    -------
+    stat : float
+        The sample MGC statistic within `[-1, 1]`.
+    opt_scale: (float, float)
+        The estimated optimal scale as an `(x, y)` pair.
+
+    """
+    m, n = stat_mgc_map.shape
+
+    # the global scale at is the statistic calculated at maximial nearest
+    # neighbors. By default, statistic and optimal scale are global.
+    stat = stat_mgc_map[m - 1][n - 1]
+    opt_scale = [m, n]
+
+    if np.linalg.norm(sig_connect) != 0:
+        # proceed only when the connected region's area is sufficiently large
+        # 0.02 is simply an empirical threshold, this can be set to 0.01 or 0.05
+        # with varying levels of performance
+        if np.sum(sig_connect) >= np.ceil(0.02 * max(m, n)) * min(m, n):
+            max_corr = max(stat_mgc_map[sig_connect])
+
+            # find all scales within significant_connected_region that maximize
+            # the local correlation
+            max_corr_index = np.where((stat_mgc_map >= max_corr) & sig_connect)
+
+            if max_corr >= stat:
+                stat = max_corr
+
+                k, l = max_corr_index
+                one_d_indices = k * n + l  # 2D to 1D indexing
+                k = np.max(one_d_indices) // n
+                l = np.max(one_d_indices) % n
+                opt_scale = [k+1, l+1]  # adding 1s to match R indexing
+
+    return stat, opt_scale
+
+
+def _two_sample_transform(u, v):
+    """Helper function that concatenates x and y for two sample MGC stat.
+
+    See above for use.
+
+    Parameters
+    ----------
+    u, v : ndarray
+        `u` and `v` have shapes `(n, p)` and `(m, p)`.
+
+    Returns
+    -------
+    x : ndarray
+        Concatenate `u` and `v` along the `axis = 0`. `x` thus has shape
+        `(2n, p)`.
+    y : ndarray
+        Label matrix for `x` where 0 refers to samples that comes from `u` and
+        1 refers to samples that come from `v`. `y` thus has shape `(2n, 1)`.
+
+    """
+    nx = u.shape[0]
+    ny = v.shape[0]
+    x = np.concatenate([u, v], axis=0)
+    y = np.concatenate([np.zeros(nx), np.ones(ny)], axis=0).reshape(-1, 1)
+    return x, y

parrot/lib/python3.10/site-packages/scipy/stats/_mstats_extras.py

@@ -0,0 +1,521 @@
+"""
+Additional statistics functions with support for masked arrays.
+
+"""
+
+# Original author (2007): Pierre GF Gerard-Marchant
+
+
+__all__ = ['compare_medians_ms',
+           'hdquantiles', 'hdmedian', 'hdquantiles_sd',
+           'idealfourths',
+           'median_cihs','mjci','mquantiles_cimj',
+           'rsh',
+           'trimmed_mean_ci',]
+
+
+import numpy as np
+from numpy import float64, ndarray
+
+import numpy.ma as ma
+from numpy.ma import MaskedArray
+
+from . import _mstats_basic as mstats
+
+from scipy.stats.distributions import norm, beta, t, binom
+
+
+def hdquantiles(data, prob=list([.25,.5,.75]), axis=None, var=False,):
+    """
+    Computes quantile estimates with the Harrell-Davis method.
+
+    The quantile estimates are calculated as a weighted linear combination
+    of order statistics.
+
+    Parameters
+    ----------
+    data : array_like
+        Data array.
+    prob : sequence, optional
+        Sequence of probabilities at which to compute the quantiles.
+    axis : int or None, optional
+        Axis along which to compute the quantiles. If None, use a flattened
+        array.
+    var : bool, optional
+        Whether to return the variance of the estimate.
+
+    Returns
+    -------
+    hdquantiles : MaskedArray
+        A (p,) array of quantiles (if `var` is False), or a (2,p) array of
+        quantiles and variances (if `var` is True), where ``p`` is the
+        number of quantiles.
+
+    See Also
+    --------
+    hdquantiles_sd
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats.mstats import hdquantiles
+    >>>
+    >>> # Sample data
+    >>> data = np.array([1.2, 2.5, 3.7, 4.0, 5.1, 6.3, 7.0, 8.2, 9.4])
+    >>>
+    >>> # Probabilities at which to compute quantiles
+    >>> probabilities = [0.25, 0.5, 0.75]
+    >>>
+    >>> # Compute Harrell-Davis quantile estimates
+    >>> quantile_estimates = hdquantiles(data, prob=probabilities)
+    >>>
+    >>> # Display the quantile estimates
+    >>> for i, quantile in enumerate(probabilities):
+    ...     print(f"{int(quantile * 100)}th percentile: {quantile_estimates[i]}")
+    25th percentile: 3.1505820231763066 # may vary
+    50th percentile: 5.194344084883956
+    75th percentile: 7.430626414674935
+
+    """
+    def _hd_1D(data,prob,var):
+        "Computes the HD quantiles for a 1D array. Returns nan for invalid data."
+        xsorted = np.squeeze(np.sort(data.compressed().view(ndarray)))
+        # Don't use length here, in case we have a numpy scalar
+        n = xsorted.size
+
+        hd = np.empty((2,len(prob)), float64)
+        if n < 2:
+            hd.flat = np.nan
+            if var:
+                return hd
+            return hd[0]
+
+        v = np.arange(n+1) / float(n)
+        betacdf = beta.cdf
+        for (i,p) in enumerate(prob):
+            _w = betacdf(v, (n+1)*p, (n+1)*(1-p))
+            w = _w[1:] - _w[:-1]
+            hd_mean = np.dot(w, xsorted)
+            hd[0,i] = hd_mean
+            #
+            hd[1,i] = np.dot(w, (xsorted-hd_mean)**2)
+            #
+        hd[0, prob == 0] = xsorted[0]
+        hd[0, prob == 1] = xsorted[-1]
+        if var:
+            hd[1, prob == 0] = hd[1, prob == 1] = np.nan
+            return hd
+        return hd[0]
+    # Initialization & checks
+    data = ma.array(data, copy=False, dtype=float64)
+    p = np.atleast_1d(np.asarray(prob))
+    # Computes quantiles along axis (or globally)
+    if (axis is None) or (data.ndim == 1):
+        result = _hd_1D(data, p, var)
+    else:
+        if data.ndim > 2:
+            raise ValueError("Array 'data' must be at most two dimensional, "
+                             "but got data.ndim = %d" % data.ndim)
+        result = ma.apply_along_axis(_hd_1D, axis, data, p, var)
+
+    return ma.fix_invalid(result, copy=False)
+
+
+def hdmedian(data, axis=-1, var=False):
+    """
+    Returns the Harrell-Davis estimate of the median along the given axis.
+
+    Parameters
+    ----------
+    data : ndarray
+        Data array.
+    axis : int, optional
+        Axis along which to compute the quantiles. If None, use a flattened
+        array.
+    var : bool, optional
+        Whether to return the variance of the estimate.
+
+    Returns
+    -------
+    hdmedian : MaskedArray
+        The median values.  If ``var=True``, the variance is returned inside
+        the masked array.  E.g. for a 1-D array the shape change from (1,) to
+        (2,).
+
+    """
+    result = hdquantiles(data,[0.5], axis=axis, var=var)
+    return result.squeeze()
+
+
+def hdquantiles_sd(data, prob=list([.25,.5,.75]), axis=None):
+    """
+    The standard error of the Harrell-Davis quantile estimates by jackknife.
+
+    Parameters
+    ----------
+    data : array_like
+        Data array.
+    prob : sequence, optional
+        Sequence of quantiles to compute.
+    axis : int, optional
+        Axis along which to compute the quantiles. If None, use a flattened
+        array.
+
+    Returns
+    -------
+    hdquantiles_sd : MaskedArray
+        Standard error of the Harrell-Davis quantile estimates.
+
+    See Also
+    --------
+    hdquantiles
+
+    """
+    def _hdsd_1D(data, prob):
+        "Computes the std error for 1D arrays."
+        xsorted = np.sort(data.compressed())
+        n = len(xsorted)
+
+        hdsd = np.empty(len(prob), float64)
+        if n < 2:
+            hdsd.flat = np.nan
+
+        vv = np.arange(n) / float(n-1)
+        betacdf = beta.cdf
+
+        for (i,p) in enumerate(prob):
+            _w = betacdf(vv, n*p, n*(1-p))
+            w = _w[1:] - _w[:-1]
+            # cumulative sum of weights and data points if
+            # ith point is left out for jackknife
+            mx_ = np.zeros_like(xsorted)
+            mx_[1:] = np.cumsum(w * xsorted[:-1])
+            # similar but from the right
+            mx_[:-1] += np.cumsum(w[::-1] * xsorted[:0:-1])[::-1]
+            hdsd[i] = np.sqrt(mx_.var() * (n - 1))
+        return hdsd
+
+    # Initialization & checks
+    data = ma.array(data, copy=False, dtype=float64)
+    p = np.atleast_1d(np.asarray(prob))
+    # Computes quantiles along axis (or globally)
+    if (axis is None):
+        result = _hdsd_1D(data, p)
+    else:
+        if data.ndim > 2:
+            raise ValueError("Array 'data' must be at most two dimensional, "
+                             "but got data.ndim = %d" % data.ndim)
+        result = ma.apply_along_axis(_hdsd_1D, axis, data, p)
+
+    return ma.fix_invalid(result, copy=False).ravel()
+
+
+def trimmed_mean_ci(data, limits=(0.2,0.2), inclusive=(True,True),
+                    alpha=0.05, axis=None):
+    """
+    Selected confidence interval of the trimmed mean along the given axis.
+
+    Parameters
+    ----------
+    data : array_like
+        Input data.
+    limits : {None, tuple}, optional
+        None or a two item tuple.
+        Tuple of the percentages to cut on each side of the array, with respect
+        to the number of unmasked data, as floats between 0. and 1. If ``n``
+        is the number of unmasked data before trimming, then
+        (``n * limits[0]``)th smallest data and (``n * limits[1]``)th
+        largest data are masked.  The total number of unmasked data after
+        trimming is ``n * (1. - sum(limits))``.
+        The value of one limit can be set to None to indicate an open interval.
+
+        Defaults to (0.2, 0.2).
+    inclusive : (2,) tuple of boolean, optional
+        If relative==False, tuple indicating whether values exactly equal to
+        the absolute limits are allowed.
+        If relative==True, tuple indicating whether the number of data being
+        masked on each side should be rounded (True) or truncated (False).
+
+        Defaults to (True, True).
+    alpha : float, optional
+        Confidence level of the intervals.
+
+        Defaults to 0.05.
+    axis : int, optional
+        Axis along which to cut. If None, uses a flattened version of `data`.
+
+        Defaults to None.
+
+    Returns
+    -------
+    trimmed_mean_ci : (2,) ndarray
+        The lower and upper confidence intervals of the trimmed data.
+
+    """
+    data = ma.array(data, copy=False)
+    trimmed = mstats.trimr(data, limits=limits, inclusive=inclusive, axis=axis)
+    tmean = trimmed.mean(axis)
+    tstde = mstats.trimmed_stde(data,limits=limits,inclusive=inclusive,axis=axis)
+    df = trimmed.count(axis) - 1
+    tppf = t.ppf(1-alpha/2.,df)
+    return np.array((tmean - tppf*tstde, tmean+tppf*tstde))
+
+
+def mjci(data, prob=[0.25,0.5,0.75], axis=None):
+    """
+    Returns the Maritz-Jarrett estimators of the standard error of selected
+    experimental quantiles of the data.
+
+    Parameters
+    ----------
+    data : ndarray
+        Data array.
+    prob : sequence, optional
+        Sequence of quantiles to compute.
+    axis : int or None, optional
+        Axis along which to compute the quantiles. If None, use a flattened
+        array.
+
+    """
+    def _mjci_1D(data, p):
+        data = np.sort(data.compressed())
+        n = data.size
+        prob = (np.array(p) * n + 0.5).astype(int)
+        betacdf = beta.cdf
+
+        mj = np.empty(len(prob), float64)
+        x = np.arange(1,n+1, dtype=float64) / n
+        y = x - 1./n
+        for (i,m) in enumerate(prob):
+            W = betacdf(x,m-1,n-m) - betacdf(y,m-1,n-m)
+            C1 = np.dot(W,data)
+            C2 = np.dot(W,data**2)
+            mj[i] = np.sqrt(C2 - C1**2)
+        return mj
+
+    data = ma.array(data, copy=False)
+    if data.ndim > 2:
+        raise ValueError("Array 'data' must be at most two dimensional, "
+                         "but got data.ndim = %d" % data.ndim)
+
+    p = np.atleast_1d(np.asarray(prob))
+    # Computes quantiles along axis (or globally)
+    if (axis is None):
+        return _mjci_1D(data, p)
+    else:
+        return ma.apply_along_axis(_mjci_1D, axis, data, p)
+
+
+def mquantiles_cimj(data, prob=[0.25,0.50,0.75], alpha=0.05, axis=None):
+    """
+    Computes the alpha confidence interval for the selected quantiles of the
+    data, with Maritz-Jarrett estimators.
+
+    Parameters
+    ----------
+    data : ndarray
+        Data array.
+    prob : sequence, optional
+        Sequence of quantiles to compute.
+    alpha : float, optional
+        Confidence level of the intervals.
+    axis : int or None, optional
+        Axis along which to compute the quantiles.
+        If None, use a flattened array.
+
+    Returns
+    -------
+    ci_lower : ndarray
+        The lower boundaries of the confidence interval.  Of the same length as
+        `prob`.
+    ci_upper : ndarray
+        The upper boundaries of the confidence interval.  Of the same length as
+        `prob`.
+
+    """
+    alpha = min(alpha, 1 - alpha)
+    z = norm.ppf(1 - alpha/2.)
+    xq = mstats.mquantiles(data, prob, alphap=0, betap=0, axis=axis)
+    smj = mjci(data, prob, axis=axis)
+    return (xq - z * smj, xq + z * smj)
+
+
+def median_cihs(data, alpha=0.05, axis=None):
+    """
+    Computes the alpha-level confidence interval for the median of the data.
+
+    Uses the Hettmasperger-Sheather method.
+
+    Parameters
+    ----------
+    data : array_like
+        Input data. Masked values are discarded. The input should be 1D only,
+        or `axis` should be set to None.
+    alpha : float, optional
+        Confidence level of the intervals.
+    axis : int or None, optional
+        Axis along which to compute the quantiles. If None, use a flattened
+        array.
+
+    Returns
+    -------
+    median_cihs
+        Alpha level confidence interval.
+
+    """
+    def _cihs_1D(data, alpha):
+        data = np.sort(data.compressed())
+        n = len(data)
+        alpha = min(alpha, 1-alpha)
+        k = int(binom._ppf(alpha/2., n, 0.5))
+        gk = binom.cdf(n-k,n,0.5) - binom.cdf(k-1,n,0.5)
+        if gk < 1-alpha:
+            k -= 1
+            gk = binom.cdf(n-k,n,0.5) - binom.cdf(k-1,n,0.5)
+        gkk = binom.cdf(n-k-1,n,0.5) - binom.cdf(k,n,0.5)
+        I = (gk - 1 + alpha)/(gk - gkk)
+        lambd = (n-k) * I / float(k + (n-2*k)*I)
+        lims = (lambd*data[k] + (1-lambd)*data[k-1],
+                lambd*data[n-k-1] + (1-lambd)*data[n-k])
+        return lims
+    data = ma.array(data, copy=False)
+    # Computes quantiles along axis (or globally)
+    if (axis is None):
+        result = _cihs_1D(data, alpha)
+    else:
+        if data.ndim > 2:
+            raise ValueError("Array 'data' must be at most two dimensional, "
+                             "but got data.ndim = %d" % data.ndim)
+        result = ma.apply_along_axis(_cihs_1D, axis, data, alpha)
+
+    return result
+
+
+def compare_medians_ms(group_1, group_2, axis=None):
+    """
+    Compares the medians from two independent groups along the given axis.
+
+    The comparison is performed using the McKean-Schrader estimate of the
+    standard error of the medians.
+
+    Parameters
+    ----------
+    group_1 : array_like
+        First dataset.  Has to be of size >=7.
+    group_2 : array_like
+        Second dataset.  Has to be of size >=7.
+    axis : int, optional
+        Axis along which the medians are estimated. If None, the arrays are
+        flattened.  If `axis` is not None, then `group_1` and `group_2`
+        should have the same shape.
+
+    Returns
+    -------
+    compare_medians_ms : {float, ndarray}
+        If `axis` is None, then returns a float, otherwise returns a 1-D
+        ndarray of floats with a length equal to the length of `group_1`
+        along `axis`.
+
+    Examples
+    --------
+
+    >>> from scipy import stats
+    >>> a = [1, 2, 3, 4, 5, 6, 7]
+    >>> b = [8, 9, 10, 11, 12, 13, 14]
+    >>> stats.mstats.compare_medians_ms(a, b, axis=None)
+    1.0693225866553746e-05
+
+    The function is vectorized to compute along a given axis.
+
+    >>> import numpy as np
+    >>> rng = np.random.default_rng()
+    >>> x = rng.random(size=(3, 7))
+    >>> y = rng.random(size=(3, 8))
+    >>> stats.mstats.compare_medians_ms(x, y, axis=1)
+    array([0.36908985, 0.36092538, 0.2765313 ])
+
+    References
+    ----------
+    .. [1] McKean, Joseph W., and Ronald M. Schrader. "A comparison of methods
+       for studentizing the sample median." Communications in
+       Statistics-Simulation and Computation 13.6 (1984): 751-773.
+
+    """
+    (med_1, med_2) = (ma.median(group_1,axis=axis), ma.median(group_2,axis=axis))
+    (std_1, std_2) = (mstats.stde_median(group_1, axis=axis),
+                      mstats.stde_median(group_2, axis=axis))
+    W = np.abs(med_1 - med_2) / ma.sqrt(std_1**2 + std_2**2)
+    return 1 - norm.cdf(W)
+
+
+def idealfourths(data, axis=None):
+    """
+    Returns an estimate of the lower and upper quartiles.
+
+    Uses the ideal fourths algorithm.
+
+    Parameters
+    ----------
+    data : array_like
+        Input array.
+    axis : int, optional
+        Axis along which the quartiles are estimated. If None, the arrays are
+        flattened.
+
+    Returns
+    -------
+    idealfourths : {list of floats, masked array}
+        Returns the two internal values that divide `data` into four parts
+        using the ideal fourths algorithm either along the flattened array
+        (if `axis` is None) or along `axis` of `data`.
+
+    """
+    def _idf(data):
+        x = data.compressed()
+        n = len(x)
+        if n < 3:
+            return [np.nan,np.nan]
+        (j,h) = divmod(n/4. + 5/12.,1)
+        j = int(j)
+        qlo = (1-h)*x[j-1] + h*x[j]
+        k = n - j
+        qup = (1-h)*x[k] + h*x[k-1]
+        return [qlo, qup]
+    data = ma.sort(data, axis=axis).view(MaskedArray)
+    if (axis is None):
+        return _idf(data)
+    else:
+        return ma.apply_along_axis(_idf, axis, data)
+
+
+def rsh(data, points=None):
+    """
+    Evaluates Rosenblatt's shifted histogram estimators for each data point.
+
+    Rosenblatt's estimator is a centered finite-difference approximation to the
+    derivative of the empirical cumulative distribution function.
+
+    Parameters
+    ----------
+    data : sequence
+        Input data, should be 1-D. Masked values are ignored.
+    points : sequence or None, optional
+        Sequence of points where to evaluate Rosenblatt shifted histogram.
+        If None, use the data.
+
+    """
+    data = ma.array(data, copy=False)
+    if points is None:
+        points = data
+    else:
+        points = np.atleast_1d(np.asarray(points))
+
+    if data.ndim != 1:
+        raise AttributeError("The input array should be 1D only !")
+
+    n = data.count()
+    r = idealfourths(data, axis=None)
+    h = 1.2 * (r[-1]-r[0]) / n**(1./5)
+    nhi = (data[:,None] <= points[None,:] + h).sum(0)
+    nlo = (data[:,None] < points[None,:] - h).sum(0)
+    return (nhi-nlo) / (2.*n*h)

parrot/lib/python3.10/site-packages/scipy/stats/_qmvnt.py

@@ -0,0 +1,533 @@
+# Integration of multivariate normal and t distributions.
+
+# Adapted from the MATLAB original implementations by Dr. Alan Genz.
+
+#     http://www.math.wsu.edu/faculty/genz/software/software.html
+
+# Copyright (C) 2013, Alan Genz,  All rights reserved.
+# Python implementation is copyright (C) 2022, Robert Kern,  All rights
+# reserved.
+
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided the following conditions are met:
+#   1. Redistributions of source code must retain the above copyright
+#      notice, this list of conditions and the following disclaimer.
+#   2. Redistributions in binary form must reproduce the above copyright
+#      notice, this list of conditions and the following disclaimer in
+#      the documentation and/or other materials provided with the
+#      distribution.
+#   3. The contributor name(s) may not be used to endorse or promote
+#      products derived from this software without specific prior
+#      written permission.
+# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+# COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+# BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+# OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
+# ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
+# TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF USE
+# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+
+import numpy as np
+
+from scipy.fft import fft, ifft
+from scipy.special import gammaincinv, ndtr, ndtri
+from scipy.stats._qmc import primes_from_2_to
+
+
+phi = ndtr
+phinv = ndtri
+
+
+def _factorize_int(n):
+    """Return a sorted list of the unique prime factors of a positive integer.
+    """
+    # NOTE: There are lots faster ways to do this, but this isn't terrible.
+    factors = set()
+    for p in primes_from_2_to(int(np.sqrt(n)) + 1):
+        while not (n % p):
+            factors.add(p)
+            n //= p
+        if n == 1:
+            break
+    if n != 1:
+        factors.add(n)
+    return sorted(factors)
+
+
+def _primitive_root(p):
+    """Compute a primitive root of the prime number `p`.
+
+    Used in the CBC lattice construction.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Primitive_root_modulo_n
+    """
+    # p is prime
+    pm = p - 1
+    factors = _factorize_int(pm)
+    n = len(factors)
+    r = 2
+    k = 0
+    while k < n:
+        d = pm // factors[k]
+        # pow() doesn't like numpy scalar types.
+        rd = pow(int(r), int(d), int(p))
+        if rd == 1:
+            r += 1
+            k = 0
+        else:
+            k += 1
+    return r
+
+
+def _cbc_lattice(n_dim, n_qmc_samples):
+    """Compute a QMC lattice generator using a Fast CBC construction.
+
+    Parameters
+    ----------
+    n_dim : int > 0
+        The number of dimensions for the lattice.
+    n_qmc_samples : int > 0
+        The desired number of QMC samples. This will be rounded down to the
+        nearest prime to enable the CBC construction.
+
+    Returns
+    -------
+    q : float array : shape=(n_dim,)
+        The lattice generator vector. All values are in the open interval
+        `(0, 1)`.
+    actual_n_qmc_samples : int
+        The prime number of QMC samples that must be used with this lattice,
+        no more, no less.
+
+    References
+    ----------
+    .. [1] Nuyens, D. and Cools, R. "Fast Component-by-Component Construction,
+           a Reprise for Different Kernels", In H. Niederreiter and D. Talay,
+           editors, Monte-Carlo and Quasi-Monte Carlo Methods 2004,
+           Springer-Verlag, 2006, 371-385.
+    """
+    # Round down to the nearest prime number.
+    primes = primes_from_2_to(n_qmc_samples + 1)
+    n_qmc_samples = primes[-1]
+
+    bt = np.ones(n_dim)
+    gm = np.hstack([1.0, 0.8 ** np.arange(n_dim - 1)])
+    q = 1
+    w = 0
+    z = np.arange(1, n_dim + 1)
+    m = (n_qmc_samples - 1) // 2
+    g = _primitive_root(n_qmc_samples)
+    # Slightly faster way to compute perm[j] = pow(g, j, n_qmc_samples)
+    # Shame that we don't have modulo pow() implemented as a ufunc.
+    perm = np.ones(m, dtype=int)
+    for j in range(m - 1):
+        perm[j + 1] = (g * perm[j]) % n_qmc_samples
+    perm = np.minimum(n_qmc_samples - perm, perm)
+    pn = perm / n_qmc_samples
+    c = pn * pn - pn + 1.0 / 6
+    fc = fft(c)
+    for s in range(1, n_dim):
+        reordered = np.hstack([
+            c[:w+1][::-1],
+            c[w+1:m][::-1],
+        ])
+        q = q * (bt[s-1] + gm[s-1] * reordered)
+        w = ifft(fc * fft(q)).real.argmin()
+        z[s] = perm[w]
+    q = z / n_qmc_samples
+    return q, n_qmc_samples
+
+
+# Note: this function is not currently used or tested by any SciPy code. It is
+# included in this file to facilitate the development of a parameter for users
+# to set the desired CDF accuracy, but must be reviewed and tested before use.
+def _qauto(func, covar, low, high, rng, error=1e-3, limit=10_000, **kwds):
+    """Automatically rerun the integration to get the required error bound.
+
+    Parameters
+    ----------
+    func : callable
+        Either :func:`_qmvn` or :func:`_qmvt`.
+    covar, low, high : array
+        As specified in :func:`_qmvn` and :func:`_qmvt`.
+    rng : Generator, optional
+        default_rng(), yada, yada
+    error : float > 0
+        The desired error bound.
+    limit : int > 0:
+        The rough limit of the number of integration points to consider. The
+        integration will stop looping once this limit has been *exceeded*.
+    **kwds :
+        Other keyword arguments to pass to `func`. When using :func:`_qmvt`, be
+        sure to include ``nu=`` as one of these.
+
+    Returns
+    -------
+    prob : float
+        The estimated probability mass within the bounds.
+    est_error : float
+        3 times the standard error of the batch estimates.
+    n_samples : int
+        The number of integration points actually used.
+    """
+    n = len(covar)
+    n_samples = 0
+    if n == 1:
+        prob = phi(high) - phi(low)
+        # More or less
+        est_error = 1e-15
+    else:
+        mi = min(limit, n * 1000)
+        prob = 0.0
+        est_error = 1.0
+        ei = 0.0
+        while est_error > error and n_samples < limit:
+            mi = round(np.sqrt(2) * mi)
+            pi, ei, ni = func(mi, covar, low, high, rng=rng, **kwds)
+            n_samples += ni
+            wt = 1.0 / (1 + (ei / est_error)**2)
+            prob += wt * (pi - prob)
+            est_error = np.sqrt(wt) * ei
+    return prob, est_error, n_samples
+
+
+# Note: this function is not currently used or tested by any SciPy code. It is
+# included in this file to facilitate the resolution of gh-8367, gh-16142, and
+# possibly gh-14286, but must be reviewed and tested before use.
+def _qmvn(m, covar, low, high, rng, lattice='cbc', n_batches=10):
+    """Multivariate normal integration over box bounds.
+
+    Parameters
+    ----------
+    m : int > n_batches
+        The number of points to sample. This number will be divided into
+        `n_batches` batches that apply random offsets of the sampling lattice
+        for each batch in order to estimate the error.
+    covar : (n, n) float array
+        Possibly singular, positive semidefinite symmetric covariance matrix.
+    low, high : (n,) float array
+        The low and high integration bounds.
+    rng : Generator, optional
+        default_rng(), yada, yada
+    lattice : 'cbc' or callable
+        The type of lattice rule to use to construct the integration points.
+    n_batches : int > 0, optional
+        The number of QMC batches to apply.
+
+    Returns
+    -------
+    prob : float
+        The estimated probability mass within the bounds.
+    est_error : float
+        3 times the standard error of the batch estimates.
+    """
+    cho, lo, hi = _permuted_cholesky(covar, low, high)
+    n = cho.shape[0]
+    ct = cho[0, 0]
+    c = phi(lo[0] / ct)
+    d = phi(hi[0] / ct)
+    ci = c
+    dci = d - ci
+    prob = 0.0
+    error_var = 0.0
+    q, n_qmc_samples = _cbc_lattice(n - 1, max(m // n_batches, 1))
+    y = np.zeros((n - 1, n_qmc_samples))
+    i_samples = np.arange(n_qmc_samples) + 1
+    for j in range(n_batches):
+        c = np.full(n_qmc_samples, ci)
+        dc = np.full(n_qmc_samples, dci)
+        pv = dc.copy()
+        for i in range(1, n):
+            # Pseudorandomly-shifted lattice coordinate.
+            z = q[i - 1] * i_samples + rng.random()
+            # Fast remainder(z, 1.0)
+            z -= z.astype(int)
+            # Tent periodization transform.
+            x = abs(2 * z - 1)
+            y[i - 1, :] = phinv(c + x * dc)
+            s = cho[i, :i] @ y[:i, :]
+            ct = cho[i, i]
+            c = phi((lo[i] - s) / ct)
+            d = phi((hi[i] - s) / ct)
+            dc = d - c
+            pv = pv * dc
+        # Accumulate the mean and error variances with online formulations.
+        d = (pv.mean() - prob) / (j + 1)
+        prob += d
+        error_var = (j - 1) * error_var / (j + 1) + d * d
+    # Error bounds are 3 times the standard error of the estimates.
+    est_error = 3 * np.sqrt(error_var)
+    n_samples = n_qmc_samples * n_batches
+    return prob, est_error, n_samples
+
+
+# Note: this function is not currently used or tested by any SciPy code. It is
+# included in this file to facilitate the resolution of gh-8367, gh-16142, and
+# possibly gh-14286, but must be reviewed and tested before use.
+def _mvn_qmc_integrand(covar, low, high, use_tent=False):
+    """Transform the multivariate normal integration into a QMC integrand over
+    a unit hypercube.
+
+    The dimensionality of the resulting hypercube integration domain is one
+    less than the dimensionality of the original integrand. Note that this
+    transformation subsumes the integration bounds in order to account for
+    infinite bounds. The QMC integration one does with the returned integrand
+    should be on the unit hypercube.
+
+    Parameters
+    ----------
+    covar : (n, n) float array
+        Possibly singular, positive semidefinite symmetric covariance matrix.
+    low, high : (n,) float array
+        The low and high integration bounds.
+    use_tent : bool, optional
+        If True, then use tent periodization. Only helpful for lattice rules.
+
+    Returns
+    -------
+    integrand : Callable[[NDArray], NDArray]
+        The QMC-integrable integrand. It takes an
+        ``(n_qmc_samples, ndim_integrand)`` array of QMC samples in the unit
+        hypercube and returns the ``(n_qmc_samples,)`` evaluations of at these
+        QMC points.
+    ndim_integrand : int
+        The dimensionality of the integrand. Equal to ``n-1``.
+    """
+    cho, lo, hi = _permuted_cholesky(covar, low, high)
+    n = cho.shape[0]
+    ndim_integrand = n - 1
+    ct = cho[0, 0]
+    c = phi(lo[0] / ct)
+    d = phi(hi[0] / ct)
+    ci = c
+    dci = d - ci
+
+    def integrand(*zs):
+        ndim_qmc = len(zs)
+        n_qmc_samples = len(np.atleast_1d(zs[0]))
+        assert ndim_qmc == ndim_integrand
+        y = np.zeros((ndim_qmc, n_qmc_samples))
+        c = np.full(n_qmc_samples, ci)
+        dc = np.full(n_qmc_samples, dci)
+        pv = dc.copy()
+        for i in range(1, n):
+            if use_tent:
+                # Tent periodization transform.
+                x = abs(2 * zs[i-1] - 1)
+            else:
+                x = zs[i-1]
+            y[i - 1, :] = phinv(c + x * dc)
+            s = cho[i, :i] @ y[:i, :]
+            ct = cho[i, i]
+            c = phi((lo[i] - s) / ct)
+            d = phi((hi[i] - s) / ct)
+            dc = d - c
+            pv = pv * dc
+        return pv
+
+    return integrand, ndim_integrand
+
+
+def _qmvt(m, nu, covar, low, high, rng, lattice='cbc', n_batches=10):
+    """Multivariate t integration over box bounds.
+
+    Parameters
+    ----------
+    m : int > n_batches
+        The number of points to sample. This number will be divided into
+        `n_batches` batches that apply random offsets of the sampling lattice
+        for each batch in order to estimate the error.
+    nu : float >= 0
+        The shape parameter of the multivariate t distribution.
+    covar : (n, n) float array
+        Possibly singular, positive semidefinite symmetric covariance matrix.
+    low, high : (n,) float array
+        The low and high integration bounds.
+    rng : Generator, optional
+        default_rng(), yada, yada
+    lattice : 'cbc' or callable
+        The type of lattice rule to use to construct the integration points.
+    n_batches : int > 0, optional
+        The number of QMC batches to apply.
+
+    Returns
+    -------
+    prob : float
+        The estimated probability mass within the bounds.
+    est_error : float
+        3 times the standard error of the batch estimates.
+    n_samples : int
+        The number of samples actually used.
+    """
+    sn = max(1.0, np.sqrt(nu))
+    low = np.asarray(low, dtype=np.float64)
+    high = np.asarray(high, dtype=np.float64)
+    cho, lo, hi = _permuted_cholesky(covar, low / sn, high / sn)
+    n = cho.shape[0]
+    prob = 0.0
+    error_var = 0.0
+    q, n_qmc_samples = _cbc_lattice(n, max(m // n_batches, 1))
+    i_samples = np.arange(n_qmc_samples) + 1
+    for j in range(n_batches):
+        pv = np.ones(n_qmc_samples)
+        s = np.zeros((n, n_qmc_samples))
+        for i in range(n):
+            # Pseudorandomly-shifted lattice coordinate.
+            z = q[i] * i_samples + rng.random()
+            # Fast remainder(z, 1.0)
+            z -= z.astype(int)
+            # Tent periodization transform.
+            x = abs(2 * z - 1)
+            # FIXME: Lift the i==0 case out of the loop to make the logic
+            # easier to follow.
+            if i == 0:
+                # We'll use one of the QR variates to pull out the
+                # t-distribution scaling.
+                if nu > 0:
+                    r = np.sqrt(2 * gammaincinv(nu / 2, x))
+                else:
+                    r = np.ones_like(x)
+            else:
+                y = phinv(c + x * dc)  # noqa: F821
+                with np.errstate(invalid='ignore'):
+                    s[i:, :] += cho[i:, i - 1][:, np.newaxis] * y
+            si = s[i, :]
+
+            c = np.ones(n_qmc_samples)
+            d = np.ones(n_qmc_samples)
+            with np.errstate(invalid='ignore'):
+                lois = lo[i] * r - si
+                hiis = hi[i] * r - si
+            c[lois < -9] = 0.0
+            d[hiis < -9] = 0.0
+            lo_mask = abs(lois) < 9
+            hi_mask = abs(hiis) < 9
+            c[lo_mask] = phi(lois[lo_mask])
+            d[hi_mask] = phi(hiis[hi_mask])
+
+            dc = d - c
+            pv *= dc
+
+        # Accumulate the mean and error variances with online formulations.
+        d = (pv.mean() - prob) / (j + 1)
+        prob += d
+        error_var = (j - 1) * error_var / (j + 1) + d * d
+    # Error bounds are 3 times the standard error of the estimates.
+    est_error = 3 * np.sqrt(error_var)
+    n_samples = n_qmc_samples * n_batches
+    return prob, est_error, n_samples
+
+
+def _permuted_cholesky(covar, low, high, tol=1e-10):
+    """Compute a scaled, permuted Cholesky factor, with integration bounds.
+
+    The scaling and permuting of the dimensions accomplishes part of the
+    transformation of the original integration problem into a more numerically
+    tractable form. The lower-triangular Cholesky factor will then be used in
+    the subsequent integration. The integration bounds will be scaled and
+    permuted as well.
+
+    Parameters
+    ----------
+    covar : (n, n) float array
+        Possibly singular, positive semidefinite symmetric covariance matrix.
+    low, high : (n,) float array
+        The low and high integration bounds.
+    tol : float, optional
+        The singularity tolerance.
+
+    Returns
+    -------
+    cho : (n, n) float array
+        Lower Cholesky factor, scaled and permuted.
+    new_low, new_high : (n,) float array
+        The scaled and permuted low and high integration bounds.
+    """
+    # Make copies for outputting.
+    cho = np.array(covar, dtype=np.float64)
+    new_lo = np.array(low, dtype=np.float64)
+    new_hi = np.array(high, dtype=np.float64)
+    n = cho.shape[0]
+    if cho.shape != (n, n):
+        raise ValueError("expected a square symmetric array")
+    if new_lo.shape != (n,) or new_hi.shape != (n,):
+        raise ValueError(
+            "expected integration boundaries the same dimensions "
+            "as the covariance matrix"
+        )
+    # Scale by the sqrt of the diagonal.
+    dc = np.sqrt(np.maximum(np.diag(cho), 0.0))
+    # But don't divide by 0.
+    dc[dc == 0.0] = 1.0
+    new_lo /= dc
+    new_hi /= dc
+    cho /= dc
+    cho /= dc[:, np.newaxis]
+
+    y = np.zeros(n)
+    sqtp = np.sqrt(2 * np.pi)
+    for k in range(n):
+        epk = (k + 1) * tol
+        im = k
+        ck = 0.0
+        dem = 1.0
+        s = 0.0
+        lo_m = 0.0
+        hi_m = 0.0
+        for i in range(k, n):
+            if cho[i, i] > tol:
+                ci = np.sqrt(cho[i, i])
+                if i > 0:
+                    s = cho[i, :k] @ y[:k]
+                lo_i = (new_lo[i] - s) / ci
+                hi_i = (new_hi[i] - s) / ci
+                de = phi(hi_i) - phi(lo_i)
+                if de <= dem:
+                    ck = ci
+                    dem = de
+                    lo_m = lo_i
+                    hi_m = hi_i
+                    im = i
+        if im > k:
+            # Swap im and k
+            cho[im, im] = cho[k, k]
+            _swap_slices(cho, np.s_[im, :k], np.s_[k, :k])
+            _swap_slices(cho, np.s_[im + 1:, im], np.s_[im + 1:, k])
+            _swap_slices(cho, np.s_[k + 1:im, k], np.s_[im, k + 1:im])
+            _swap_slices(new_lo, k, im)
+            _swap_slices(new_hi, k, im)
+        if ck > epk:
+            cho[k, k] = ck
+            cho[k, k + 1:] = 0.0
+            for i in range(k + 1, n):
+                cho[i, k] /= ck
+                cho[i, k + 1:i + 1] -= cho[i, k] * cho[k + 1:i + 1, k]
+            if abs(dem) > tol:
+                y[k] = ((np.exp(-lo_m * lo_m / 2) - np.exp(-hi_m * hi_m / 2)) /
+                        (sqtp * dem))
+            else:
+                y[k] = (lo_m + hi_m) / 2
+                if lo_m < -10:
+                    y[k] = hi_m
+                elif hi_m > 10:
+                    y[k] = lo_m
+            cho[k, :k + 1] /= ck
+            new_lo[k] /= ck
+            new_hi[k] /= ck
+        else:
+            cho[k:, k] = 0.0
+            y[k] = (new_lo[k] + new_hi[k]) / 2
+    return cho, new_lo, new_hi
+
+
+def _swap_slices(x, slc1, slc2):
+    t = x[slc1].copy()
+    x[slc1] = x[slc2].copy()
+    x[slc2] = t

parrot/lib/python3.10/site-packages/scipy/stats/_rvs_sampling.py

@@ -0,0 +1,56 @@
+import warnings
+from scipy.stats.sampling import RatioUniforms
+
+def rvs_ratio_uniforms(pdf, umax, vmin, vmax, size=1, c=0, random_state=None):
+    """
+    Generate random samples from a probability density function using the
+    ratio-of-uniforms method.
+
+    .. deprecated:: 1.12.0
+        `rvs_ratio_uniforms` is deprecated in favour of
+        `scipy.stats.sampling.RatioUniforms` from version 1.12.0 and will
+        be removed in SciPy 1.15.0
+
+    Parameters
+    ----------
+    pdf : callable
+        A function with signature `pdf(x)` that is proportional to the
+        probability density function of the distribution.
+    umax : float
+        The upper bound of the bounding rectangle in the u-direction.
+    vmin : float
+        The lower bound of the bounding rectangle in the v-direction.
+    vmax : float
+        The upper bound of the bounding rectangle in the v-direction.
+    size : int or tuple of ints, optional
+        Defining number of random variates (default is 1).
+    c : float, optional.
+        Shift parameter of ratio-of-uniforms method, see Notes. Default is 0.
+    random_state : {None, int, `numpy.random.Generator`,
+                    `numpy.random.RandomState`}, optional
+
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+
+    Returns
+    -------
+    rvs : ndarray
+        The random variates distributed according to the probability
+        distribution defined by the pdf.
+
+    Notes
+    -----
+    Please refer to `scipy.stats.sampling.RatioUniforms` for the documentation.
+    """
+    warnings.warn("Please use `RatioUniforms` from the "
+                  "`scipy.stats.sampling` namespace. The "
+                  "`scipy.stats.rvs_ratio_uniforms` namespace is deprecated "
+                  "and will be removed in SciPy 1.15.0",
+                  category=DeprecationWarning, stacklevel=2)
+    gen = RatioUniforms(pdf, umax=umax, vmin=vmin, vmax=vmax,
+                        c=c, random_state=random_state)
+    return gen.rvs(size)

parrot/lib/python3.10/site-packages/scipy/stats/_sensitivity_analysis.py

@@ -0,0 +1,712 @@
+from __future__ import annotations
+
+import inspect
+from dataclasses import dataclass
+from typing import (
+    Callable, Literal, Protocol, TYPE_CHECKING
+)
+
+import numpy as np
+
+from scipy.stats._common import ConfidenceInterval
+from scipy.stats._qmc import check_random_state
+from scipy.stats._resampling import BootstrapResult
+from scipy.stats import qmc, bootstrap
+
+
+if TYPE_CHECKING:
+    import numpy.typing as npt
+    from scipy._lib._util import DecimalNumber, IntNumber, SeedType
+
+
+__all__ = [
+    'sobol_indices'
+]
+
+
+def f_ishigami(x: npt.ArrayLike) -> np.ndarray:
+    r"""Ishigami function.
+
+    .. math::
+
+        Y(\mathbf{x}) = \sin x_1 + 7 \sin^2 x_2 + 0.1 x_3^4 \sin x_1
+
+    with :math:`\mathbf{x} \in [-\pi, \pi]^3`.
+
+    Parameters
+    ----------
+    x : array_like ([x1, x2, x3], n)
+
+    Returns
+    -------
+    f : array_like (n,)
+        Function evaluation.
+
+    References
+    ----------
+    .. [1] Ishigami, T. and T. Homma. "An importance quantification technique
+       in uncertainty analysis for computer models." IEEE,
+       :doi:`10.1109/ISUMA.1990.151285`, 1990.
+    """
+    x = np.atleast_2d(x)
+    f_eval = (
+        np.sin(x[0])
+        + 7 * np.sin(x[1])**2
+        + 0.1 * (x[2]**4) * np.sin(x[0])
+    )
+    return f_eval
+
+
+def sample_A_B(
+    n: IntNumber,
+    dists: list[PPFDist],
+    random_state: SeedType = None
+) -> np.ndarray:
+    """Sample two matrices A and B.
+
+    Uses a Sobol' sequence with 2`d` columns to have 2 uncorrelated matrices.
+    This is more efficient than using 2 random draw of Sobol'.
+    See sec. 5 from [1]_.
+
+    Output shape is (d, n).
+
+    References
+    ----------
+    .. [1] Saltelli, A., P. Annoni, I. Azzini, F. Campolongo, M. Ratto, and
+       S. Tarantola. "Variance based sensitivity analysis of model
+       output. Design and estimator for the total sensitivity index."
+       Computer Physics Communications, 181(2):259-270,
+       :doi:`10.1016/j.cpc.2009.09.018`, 2010.
+    """
+    d = len(dists)
+    A_B = qmc.Sobol(d=2*d, seed=random_state, bits=64).random(n).T
+    A_B = A_B.reshape(2, d, -1)
+    try:
+        for d_, dist in enumerate(dists):
+            A_B[:, d_] = dist.ppf(A_B[:, d_])
+    except AttributeError as exc:
+        message = "Each distribution in `dists` must have method `ppf`."
+        raise ValueError(message) from exc
+    return A_B
+
+
+def sample_AB(A: np.ndarray, B: np.ndarray) -> np.ndarray:
+    """AB matrix.
+
+    AB: rows of B into A. Shape (d, d, n).
+    - Copy A into d "pages"
+    - In the first page, replace 1st rows of A with 1st row of B.
+    ...
+    - In the dth page, replace dth row of A with dth row of B.
+    - return the stack of pages
+    """
+    d, n = A.shape
+    AB = np.tile(A, (d, 1, 1))
+    i = np.arange(d)
+    AB[i, i] = B[i]
+    return AB
+
+
+def saltelli_2010(
+    f_A: np.ndarray, f_B: np.ndarray, f_AB: np.ndarray
+) -> tuple[np.ndarray, np.ndarray]:
+    r"""Saltelli2010 formulation.
+
+    .. math::
+
+        S_i = \frac{1}{N} \sum_{j=1}^N
+        f(\mathbf{B})_j (f(\mathbf{AB}^{(i)})_j - f(\mathbf{A})_j)
+
+    .. math::
+
+        S_{T_i} = \frac{1}{N} \sum_{j=1}^N
+        (f(\mathbf{A})_j - f(\mathbf{AB}^{(i)})_j)^2
+
+    Parameters
+    ----------
+    f_A, f_B : array_like (s, n)
+        Function values at A and B, respectively
+    f_AB : array_like (d, s, n)
+        Function values at each of the AB pages
+
+    Returns
+    -------
+    s, st : array_like (s, d)
+        First order and total order Sobol' indices.
+
+    References
+    ----------
+    .. [1] Saltelli, A., P. Annoni, I. Azzini, F. Campolongo, M. Ratto, and
+       S. Tarantola. "Variance based sensitivity analysis of model
+       output. Design and estimator for the total sensitivity index."
+       Computer Physics Communications, 181(2):259-270,
+       :doi:`10.1016/j.cpc.2009.09.018`, 2010.
+    """
+    # Empirical variance calculated using output from A and B which are
+    # independent. Output of AB is not independent and cannot be used
+    var = np.var([f_A, f_B], axis=(0, -1))
+
+    # We divide by the variance to have a ratio of variance
+    # this leads to eq. 2
+    s = np.mean(f_B * (f_AB - f_A), axis=-1) / var  # Table 2 (b)
+    st = 0.5 * np.mean((f_A - f_AB) ** 2, axis=-1) / var  # Table 2 (f)
+
+    return s.T, st.T
+
+
+@dataclass
+class BootstrapSobolResult:
+    first_order: BootstrapResult
+    total_order: BootstrapResult
+
+
+@dataclass
+class SobolResult:
+    first_order: np.ndarray
+    total_order: np.ndarray
+    _indices_method: Callable
+    _f_A: np.ndarray
+    _f_B: np.ndarray
+    _f_AB: np.ndarray
+    _A: np.ndarray | None = None
+    _B: np.ndarray | None = None
+    _AB: np.ndarray | None = None
+    _bootstrap_result: BootstrapResult | None = None
+
+    def bootstrap(
+        self,
+        confidence_level: DecimalNumber = 0.95,
+        n_resamples: IntNumber = 999
+    ) -> BootstrapSobolResult:
+        """Bootstrap Sobol' indices to provide confidence intervals.
+
+        Parameters
+        ----------
+        confidence_level : float, default: ``0.95``
+            The confidence level of the confidence intervals.
+        n_resamples : int, default: ``999``
+            The number of resamples performed to form the bootstrap
+            distribution of the indices.
+
+        Returns
+        -------
+        res : BootstrapSobolResult
+            Bootstrap result containing the confidence intervals and the
+            bootstrap distribution of the indices.
+
+            An object with attributes:
+
+            first_order : BootstrapResult
+                Bootstrap result of the first order indices.
+            total_order : BootstrapResult
+                Bootstrap result of the total order indices.
+            See `BootstrapResult` for more details.
+
+        """
+        def statistic(idx):
+            f_A_ = self._f_A[:, idx]
+            f_B_ = self._f_B[:, idx]
+            f_AB_ = self._f_AB[..., idx]
+            return self._indices_method(f_A_, f_B_, f_AB_)
+
+        n = self._f_A.shape[1]
+
+        res = bootstrap(
+            [np.arange(n)], statistic=statistic, method="BCa",
+            n_resamples=n_resamples,
+            confidence_level=confidence_level,
+            bootstrap_result=self._bootstrap_result
+        )
+        self._bootstrap_result = res
+
+        first_order = BootstrapResult(
+            confidence_interval=ConfidenceInterval(
+                res.confidence_interval.low[0], res.confidence_interval.high[0]
+            ),
+            bootstrap_distribution=res.bootstrap_distribution[0],
+            standard_error=res.standard_error[0],
+        )
+        total_order = BootstrapResult(
+            confidence_interval=ConfidenceInterval(
+                res.confidence_interval.low[1], res.confidence_interval.high[1]
+            ),
+            bootstrap_distribution=res.bootstrap_distribution[1],
+            standard_error=res.standard_error[1],
+        )
+
+        return BootstrapSobolResult(
+            first_order=first_order, total_order=total_order
+        )
+
+
+class PPFDist(Protocol):
+    @property
+    def ppf(self) -> Callable[..., float]:
+        ...
+
+
+def sobol_indices(
+    *,
+    func: Callable[[np.ndarray], npt.ArrayLike] |
+          dict[Literal['f_A', 'f_B', 'f_AB'], np.ndarray],
+    n: IntNumber,
+    dists: list[PPFDist] | None = None,
+    method: Callable | Literal['saltelli_2010'] = 'saltelli_2010',
+    random_state: SeedType = None
+) -> SobolResult:
+    r"""Global sensitivity indices of Sobol'.
+
+    Parameters
+    ----------
+    func : callable or dict(str, array_like)
+        If `func` is a callable, function to compute the Sobol' indices from.
+        Its signature must be::
+
+            func(x: ArrayLike) -> ArrayLike
+
+        with ``x`` of shape ``(d, n)`` and output of shape ``(s, n)`` where:
+
+        - ``d`` is the input dimensionality of `func`
+          (number of input variables),
+        - ``s`` is the output dimensionality of `func`
+          (number of output variables), and
+        - ``n`` is the number of samples (see `n` below).
+
+        Function evaluation values must be finite.
+
+        If `func` is a dictionary, contains the function evaluations from three
+        different arrays. Keys must be: ``f_A``, ``f_B`` and ``f_AB``.
+        ``f_A`` and ``f_B`` should have a shape ``(s, n)`` and ``f_AB``
+        should have a shape ``(d, s, n)``.
+        This is an advanced feature and misuse can lead to wrong analysis.
+    n : int
+        Number of samples used to generate the matrices ``A`` and ``B``.
+        Must be a power of 2. The total number of points at which `func` is
+        evaluated will be ``n*(d+2)``.
+    dists : list(distributions), optional
+        List of each parameter's distribution. The distribution of parameters
+        depends on the application and should be carefully chosen.
+        Parameters are assumed to be independently distributed, meaning there
+        is no constraint nor relationship between their values.
+
+        Distributions must be an instance of a class with a ``ppf``
+        method.
+
+        Must be specified if `func` is a callable, and ignored otherwise.
+    method : Callable or str, default: 'saltelli_2010'
+        Method used to compute the first and total Sobol' indices.
+
+        If a callable, its signature must be::
+
+            func(f_A: np.ndarray, f_B: np.ndarray, f_AB: np.ndarray)
+            -> Tuple[np.ndarray, np.ndarray]
+
+        with ``f_A, f_B`` of shape ``(s, n)`` and ``f_AB`` of shape
+        ``(d, s, n)``.
+        These arrays contain the function evaluations from three different sets
+        of samples.
+        The output is a tuple of the first and total indices with
+        shape ``(s, d)``.
+        This is an advanced feature and misuse can lead to wrong analysis.
+    random_state : {None, int, `numpy.random.Generator`}, optional
+        If `random_state` is an int or None, a new `numpy.random.Generator` is
+        created using ``np.random.default_rng(random_state)``.
+        If `random_state` is already a ``Generator`` instance, then the
+        provided instance is used.
+
+    Returns
+    -------
+    res : SobolResult
+        An object with attributes:
+
+        first_order : ndarray of shape (s, d)
+            First order Sobol' indices.
+        total_order : ndarray of shape (s, d)
+            Total order Sobol' indices.
+
+        And method:
+
+        bootstrap(confidence_level: float, n_resamples: int)
+        -> BootstrapSobolResult
+
+            A method providing confidence intervals on the indices.
+            See `scipy.stats.bootstrap` for more details.
+
+            The bootstrapping is done on both first and total order indices,
+            and they are available in `BootstrapSobolResult` as attributes
+            ``first_order`` and ``total_order``.
+
+    Notes
+    -----
+    The Sobol' method [1]_, [2]_ is a variance-based Sensitivity Analysis which
+    obtains the contribution of each parameter to the variance of the
+    quantities of interest (QoIs; i.e., the outputs of `func`).
+    Respective contributions can be used to rank the parameters and
+    also gauge the complexity of the model by computing the
+    model's effective (or mean) dimension.
+
+    .. note::
+
+        Parameters are assumed to be independently distributed. Each
+        parameter can still follow any distribution. In fact, the distribution
+        is very important and should match the real distribution of the
+        parameters.
+
+    It uses a functional decomposition of the variance of the function to
+    explore
+
+    .. math::
+
+        \mathbb{V}(Y) = \sum_{i}^{d} \mathbb{V}_i (Y) + \sum_{i<j}^{d}
+        \mathbb{V}_{ij}(Y) + ... + \mathbb{V}_{1,2,...,d}(Y),
+
+    introducing conditional variances:
+
+    .. math::
+
+        \mathbb{V}_i(Y) = \mathbb{\mathbb{V}}[\mathbb{E}(Y|x_i)]
+        \qquad
+        \mathbb{V}_{ij}(Y) = \mathbb{\mathbb{V}}[\mathbb{E}(Y|x_i x_j)]
+        - \mathbb{V}_i(Y) - \mathbb{V}_j(Y),
+
+    Sobol' indices are expressed as
+
+    .. math::
+
+        S_i = \frac{\mathbb{V}_i(Y)}{\mathbb{V}[Y]}
+        \qquad
+        S_{ij} =\frac{\mathbb{V}_{ij}(Y)}{\mathbb{V}[Y]}.
+
+    :math:`S_{i}` corresponds to the first-order term which apprises the
+    contribution of the i-th parameter, while :math:`S_{ij}` corresponds to the
+    second-order term which informs about the contribution of interactions
+    between the i-th and the j-th parameters. These equations can be
+    generalized to compute higher order terms; however, they are expensive to
+    compute and their interpretation is complex.
+    This is why only first order indices are provided.
+
+    Total order indices represent the global contribution of the parameters
+    to the variance of the QoI and are defined as:
+
+    .. math::
+
+        S_{T_i} = S_i + \sum_j S_{ij} + \sum_{j,k} S_{ijk} + ...
+        = 1 - \frac{\mathbb{V}[\mathbb{E}(Y|x_{\sim i})]}{\mathbb{V}[Y]}.
+
+    First order indices sum to at most 1, while total order indices sum to at
+    least 1. If there are no interactions, then first and total order indices
+    are equal, and both first and total order indices sum to 1.
+
+    .. warning::
+
+        Negative Sobol' values are due to numerical errors. Increasing the
+        number of points `n` should help.
+
+        The number of sample required to have a good analysis increases with
+        the dimensionality of the problem. e.g. for a 3 dimension problem,
+        consider at minima ``n >= 2**12``. The more complex the model is,
+        the more samples will be needed.
+
+        Even for a purely addiditive model, the indices may not sum to 1 due
+        to numerical noise.
+
+    References
+    ----------
+    .. [1] Sobol, I. M.. "Sensitivity analysis for nonlinear mathematical
+       models." Mathematical Modeling and Computational Experiment, 1:407-414,
+       1993.
+    .. [2] Sobol, I. M. (2001). "Global sensitivity indices for nonlinear
+       mathematical models and their Monte Carlo estimates." Mathematics
+       and Computers in Simulation, 55(1-3):271-280,
+       :doi:`10.1016/S0378-4754(00)00270-6`, 2001.
+    .. [3] Saltelli, A. "Making best use of model evaluations to
+       compute sensitivity indices."  Computer Physics Communications,
+       145(2):280-297, :doi:`10.1016/S0010-4655(02)00280-1`, 2002.
+    .. [4] Saltelli, A., M. Ratto, T. Andres, F. Campolongo, J. Cariboni,
+       D. Gatelli, M. Saisana, and S. Tarantola. "Global Sensitivity Analysis.
+       The Primer." 2007.
+    .. [5] Saltelli, A., P. Annoni, I. Azzini, F. Campolongo, M. Ratto, and
+       S. Tarantola. "Variance based sensitivity analysis of model
+       output. Design and estimator for the total sensitivity index."
+       Computer Physics Communications, 181(2):259-270,
+       :doi:`10.1016/j.cpc.2009.09.018`, 2010.
+    .. [6] Ishigami, T. and T. Homma. "An importance quantification technique
+       in uncertainty analysis for computer models." IEEE,
+       :doi:`10.1109/ISUMA.1990.151285`, 1990.
+
+    Examples
+    --------
+    The following is an example with the Ishigami function [6]_
+
+    .. math::
+
+        Y(\mathbf{x}) = \sin x_1 + 7 \sin^2 x_2 + 0.1 x_3^4 \sin x_1,
+
+    with :math:`\mathbf{x} \in [-\pi, \pi]^3`. This function exhibits strong
+    non-linearity and non-monotonicity.
+
+    Remember, Sobol' indices assumes that samples are independently
+    distributed. In this case we use a uniform distribution on each marginals.
+
+    >>> import numpy as np
+    >>> from scipy.stats import sobol_indices, uniform
+    >>> rng = np.random.default_rng()
+    >>> def f_ishigami(x):
+    ...     f_eval = (
+    ...         np.sin(x[0])
+    ...         + 7 * np.sin(x[1])**2
+    ...         + 0.1 * (x[2]**4) * np.sin(x[0])
+    ...     )
+    ...     return f_eval
+    >>> indices = sobol_indices(
+    ...     func=f_ishigami, n=1024,
+    ...     dists=[
+    ...         uniform(loc=-np.pi, scale=2*np.pi),
+    ...         uniform(loc=-np.pi, scale=2*np.pi),
+    ...         uniform(loc=-np.pi, scale=2*np.pi)
+    ...     ],
+    ...     random_state=rng
+    ... )
+    >>> indices.first_order
+    array([0.31637954, 0.43781162, 0.00318825])
+    >>> indices.total_order
+    array([0.56122127, 0.44287857, 0.24229595])
+
+    Confidence interval can be obtained using bootstrapping.
+
+    >>> boot = indices.bootstrap()
+
+    Then, this information can be easily visualized.
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig, axs = plt.subplots(1, 2, figsize=(9, 4))
+    >>> _ = axs[0].errorbar(
+    ...     [1, 2, 3], indices.first_order, fmt='o',
+    ...     yerr=[
+    ...         indices.first_order - boot.first_order.confidence_interval.low,
+    ...         boot.first_order.confidence_interval.high - indices.first_order
+    ...     ],
+    ... )
+    >>> axs[0].set_ylabel("First order Sobol' indices")
+    >>> axs[0].set_xlabel('Input parameters')
+    >>> axs[0].set_xticks([1, 2, 3])
+    >>> _ = axs[1].errorbar(
+    ...     [1, 2, 3], indices.total_order, fmt='o',
+    ...     yerr=[
+    ...         indices.total_order - boot.total_order.confidence_interval.low,
+    ...         boot.total_order.confidence_interval.high - indices.total_order
+    ...     ],
+    ... )
+    >>> axs[1].set_ylabel("Total order Sobol' indices")
+    >>> axs[1].set_xlabel('Input parameters')
+    >>> axs[1].set_xticks([1, 2, 3])
+    >>> plt.tight_layout()
+    >>> plt.show()
+
+    .. note::
+
+        By default, `scipy.stats.uniform` has support ``[0, 1]``.
+        Using the parameters ``loc`` and ``scale``, one obtains the uniform
+        distribution on ``[loc, loc + scale]``.
+
+    This result is particularly interesting because the first order index
+    :math:`S_{x_3} = 0` whereas its total order is :math:`S_{T_{x_3}} = 0.244`.
+    This means that higher order interactions with :math:`x_3` are responsible
+    for the difference. Almost 25% of the observed variance
+    on the QoI is due to the correlations between :math:`x_3` and :math:`x_1`,
+    although :math:`x_3` by itself has no impact on the QoI.
+
+    The following gives a visual explanation of Sobol' indices on this
+    function. Let's generate 1024 samples in :math:`[-\pi, \pi]^3` and
+    calculate the value of the output.
+
+    >>> from scipy.stats import qmc
+    >>> n_dim = 3
+    >>> p_labels = ['$x_1$', '$x_2$', '$x_3$']
+    >>> sample = qmc.Sobol(d=n_dim, seed=rng).random(1024)
+    >>> sample = qmc.scale(
+    ...     sample=sample,
+    ...     l_bounds=[-np.pi, -np.pi, -np.pi],
+    ...     u_bounds=[np.pi, np.pi, np.pi]
+    ... )
+    >>> output = f_ishigami(sample.T)
+
+    Now we can do scatter plots of the output with respect to each parameter.
+    This gives a visual way to understand how each parameter impacts the
+    output of the function.
+
+    >>> fig, ax = plt.subplots(1, n_dim, figsize=(12, 4))
+    >>> for i in range(n_dim):
+    ...     xi = sample[:, i]
+    ...     ax[i].scatter(xi, output, marker='+')
+    ...     ax[i].set_xlabel(p_labels[i])
+    >>> ax[0].set_ylabel('Y')
+    >>> plt.tight_layout()
+    >>> plt.show()
+
+    Now Sobol' goes a step further:
+    by conditioning the output value by given values of the parameter
+    (black lines), the conditional output mean is computed. It corresponds to
+    the term :math:`\mathbb{E}(Y|x_i)`. Taking the variance of this term gives
+    the numerator of the Sobol' indices.
+
+    >>> mini = np.min(output)
+    >>> maxi = np.max(output)
+    >>> n_bins = 10
+    >>> bins = np.linspace(-np.pi, np.pi, num=n_bins, endpoint=False)
+    >>> dx = bins[1] - bins[0]
+    >>> fig, ax = plt.subplots(1, n_dim, figsize=(12, 4))
+    >>> for i in range(n_dim):
+    ...     xi = sample[:, i]
+    ...     ax[i].scatter(xi, output, marker='+')
+    ...     ax[i].set_xlabel(p_labels[i])
+    ...     for bin_ in bins:
+    ...         idx = np.where((bin_ <= xi) & (xi <= bin_ + dx))
+    ...         xi_ = xi[idx]
+    ...         y_ = output[idx]
+    ...         ave_y_ = np.mean(y_)
+    ...         ax[i].plot([bin_ + dx/2] * 2, [mini, maxi], c='k')
+    ...         ax[i].scatter(bin_ + dx/2, ave_y_, c='r')
+    >>> ax[0].set_ylabel('Y')
+    >>> plt.tight_layout()
+    >>> plt.show()
+
+    Looking at :math:`x_3`, the variance
+    of the mean is zero leading to :math:`S_{x_3} = 0`. But we can further
+    observe that the variance of the output is not constant along the parameter
+    values of :math:`x_3`. This heteroscedasticity is explained by higher order
+    interactions. Moreover, an heteroscedasticity is also noticeable on
+    :math:`x_1` leading to an interaction between :math:`x_3` and :math:`x_1`.
+    On :math:`x_2`, the variance seems to be constant and thus null interaction
+    with this parameter can be supposed.
+
+    This case is fairly simple to analyse visually---although it is only a
+    qualitative analysis. Nevertheless, when the number of input parameters
+    increases such analysis becomes unrealistic as it would be difficult to
+    conclude on high-order terms. Hence the benefit of using Sobol' indices.
+
+    """
+    random_state = check_random_state(random_state)
+
+    n_ = int(n)
+    if not (n_ & (n_ - 1) == 0) or n != n_:
+        raise ValueError(
+            "The balance properties of Sobol' points require 'n' "
+            "to be a power of 2."
+        )
+    n = n_
+
+    if not callable(method):
+        indices_methods: dict[str, Callable] = {
+            "saltelli_2010": saltelli_2010,
+        }
+        try:
+            method = method.lower()  # type: ignore[assignment]
+            indices_method_ = indices_methods[method]
+        except KeyError as exc:
+            message = (
+                f"{method!r} is not a valid 'method'. It must be one of"
+                f" {set(indices_methods)!r} or a callable."
+            )
+            raise ValueError(message) from exc
+    else:
+        indices_method_ = method
+        sig = inspect.signature(indices_method_)
+
+        if set(sig.parameters) != {'f_A', 'f_B', 'f_AB'}:
+            message = (
+                "If 'method' is a callable, it must have the following"
+                f" signature: {inspect.signature(saltelli_2010)}"
+            )
+            raise ValueError(message)
+
+    def indices_method(f_A, f_B, f_AB):
+        """Wrap indices method to ensure proper output dimension.
+
+        1D when single output, 2D otherwise.
+        """
+        return np.squeeze(indices_method_(f_A=f_A, f_B=f_B, f_AB=f_AB))
+
+    if callable(func):
+        if dists is None:
+            raise ValueError(
+                "'dists' must be defined when 'func' is a callable."
+            )
+
+        def wrapped_func(x):
+            return np.atleast_2d(func(x))
+
+        A, B = sample_A_B(n=n, dists=dists, random_state=random_state)
+        AB = sample_AB(A=A, B=B)
+
+        f_A = wrapped_func(A)
+
+        if f_A.shape[1] != n:
+            raise ValueError(
+                "'func' output should have a shape ``(s, -1)`` with ``s`` "
+                "the number of output."
+            )
+
+        def funcAB(AB):
+            d, d, n = AB.shape
+            AB = np.moveaxis(AB, 0, -1).reshape(d, n*d)
+            f_AB = wrapped_func(AB)
+            return np.moveaxis(f_AB.reshape((-1, n, d)), -1, 0)
+
+        f_B = wrapped_func(B)
+        f_AB = funcAB(AB)
+    else:
+        message = (
+            "When 'func' is a dictionary, it must contain the following "
+            "keys: 'f_A', 'f_B' and 'f_AB'."
+            "'f_A' and 'f_B' should have a shape ``(s, n)`` and 'f_AB' "
+            "should have a shape ``(d, s, n)``."
+        )
+        try:
+            f_A, f_B, f_AB = np.atleast_2d(
+                func['f_A'], func['f_B'], func['f_AB']
+            )
+        except KeyError as exc:
+            raise ValueError(message) from exc
+
+        if f_A.shape[1] != n or f_A.shape != f_B.shape or \
+                f_AB.shape == f_A.shape or f_AB.shape[-1] % n != 0:
+            raise ValueError(message)
+
+    # Normalization by mean
+    # Sobol', I. and Levitan, Y. L. (1999). On the use of variance reducing
+    # multipliers in monte carlo computations of a global sensitivity index.
+    # Computer Physics Communications, 117(1) :52-61.
+    mean = np.mean([f_A, f_B], axis=(0, -1)).reshape(-1, 1)
+    f_A -= mean
+    f_B -= mean
+    f_AB -= mean
+
+    # Compute indices
+    # Filter warnings for constant output as var = 0
+    with np.errstate(divide='ignore', invalid='ignore'):
+        first_order, total_order = indices_method(f_A=f_A, f_B=f_B, f_AB=f_AB)
+
+    # null variance means null indices
+    first_order[~np.isfinite(first_order)] = 0
+    total_order[~np.isfinite(total_order)] = 0
+
+    res = dict(
+        first_order=first_order,
+        total_order=total_order,
+        _indices_method=indices_method,
+        _f_A=f_A,
+        _f_B=f_B,
+        _f_AB=f_AB
+    )
+
+    if callable(func):
+        res.update(
+            dict(
+                _A=A,
+                _B=B,
+                _AB=AB,
+            )
+        )
+
+    return SobolResult(**res)

parrot/lib/python3.10/site-packages/scipy/stats/_sobol.pyi

@@ -0,0 +1,54 @@
+import numpy as np
+from scipy._lib._util import IntNumber
+from typing import Literal
+
+def _initialize_v(
+    v : np.ndarray, 
+    dim : IntNumber,
+    bits: IntNumber
+) -> None: ...
+
+def _cscramble (
+    dim : IntNumber,
+    bits: IntNumber,
+    ltm : np.ndarray,
+    sv: np.ndarray
+) -> None: ...
+
+def _fill_p_cumulative(
+    p: np.ndarray,
+    p_cumulative: np.ndarray
+) -> None: ...
+
+def _draw(
+    n : IntNumber,
+    num_gen: IntNumber,
+    dim: IntNumber,
+    scale: float,
+    sv: np.ndarray,
+    quasi: np.ndarray,
+    sample: np.ndarray
+    ) -> None: ...
+
+def _fast_forward(
+    n: IntNumber,
+    num_gen: IntNumber,
+    dim: IntNumber,
+    sv: np.ndarray,
+    quasi: np.ndarray
+    ) -> None: ...
+
+def _categorize(
+    draws: np.ndarray,
+    p_cumulative: np.ndarray,
+    result: np.ndarray
+    ) -> None: ...
+
+_MAXDIM: Literal[21201]
+_MAXDEG: Literal[18]
+
+def _test_find_index(
+    p_cumulative: np.ndarray, 
+    size: int, 
+    value: float
+    ) -> int: ...

parrot/lib/python3.10/site-packages/scipy/stats/_survival.py

@@ -0,0 +1,686 @@
+from __future__ import annotations
+
+from dataclasses import dataclass, field
+from typing import TYPE_CHECKING
+import warnings
+
+import numpy as np
+from scipy import special, interpolate, stats
+from scipy.stats._censored_data import CensoredData
+from scipy.stats._common import ConfidenceInterval
+
+if TYPE_CHECKING:
+    from typing import Literal
+    import numpy.typing as npt
+
+
+__all__ = ['ecdf', 'logrank']
+
+
+@dataclass
+class EmpiricalDistributionFunction:
+    """An empirical distribution function produced by `scipy.stats.ecdf`
+
+    Attributes
+    ----------
+    quantiles : ndarray
+        The unique values of the sample from which the
+        `EmpiricalDistributionFunction` was estimated.
+    probabilities : ndarray
+        The point estimates of the cumulative distribution function (CDF) or
+        its complement, the survival function (SF), corresponding with
+        `quantiles`.
+    """
+    quantiles: np.ndarray
+    probabilities: np.ndarray
+    # Exclude these from __str__
+    _n: np.ndarray = field(repr=False)  # number "at risk"
+    _d: np.ndarray = field(repr=False)  # number of "deaths"
+    _sf: np.ndarray = field(repr=False)  # survival function for var estimate
+    _kind: str = field(repr=False)  # type of function: "cdf" or "sf"
+
+    def __init__(self, q, p, n, d, kind):
+        self.probabilities = p
+        self.quantiles = q
+        self._n = n
+        self._d = d
+        self._sf = p if kind == 'sf' else 1 - p
+        self._kind = kind
+
+        f0 = 1 if kind == 'sf' else 0  # leftmost function value
+        f1 = 1 - f0
+        # fill_value can't handle edge cases at infinity
+        x = np.insert(q, [0, len(q)], [-np.inf, np.inf])
+        y = np.insert(p, [0, len(p)], [f0, f1])
+        # `or` conditions handle the case of empty x, points
+        self._f = interpolate.interp1d(x, y, kind='previous',
+                                       assume_sorted=True)
+
+    def evaluate(self, x):
+        """Evaluate the empirical CDF/SF function at the input.
+
+        Parameters
+        ----------
+        x : ndarray
+            Argument to the CDF/SF
+
+        Returns
+        -------
+        y : ndarray
+            The CDF/SF evaluated at the input
+        """
+        return self._f(x)
+
+    def plot(self, ax=None, **matplotlib_kwargs):
+        """Plot the empirical distribution function
+
+        Available only if ``matplotlib`` is installed.
+
+        Parameters
+        ----------
+        ax : matplotlib.axes.Axes
+            Axes object to draw the plot onto, otherwise uses the current Axes.
+
+        **matplotlib_kwargs : dict, optional
+            Keyword arguments passed directly to `matplotlib.axes.Axes.step`.
+            Unless overridden, ``where='post'``.
+
+        Returns
+        -------
+        lines : list of `matplotlib.lines.Line2D`
+            Objects representing the plotted data
+        """
+        try:
+            import matplotlib  # noqa: F401
+        except ModuleNotFoundError as exc:
+            message = "matplotlib must be installed to use method `plot`."
+            raise ModuleNotFoundError(message) from exc
+
+        if ax is None:
+            import matplotlib.pyplot as plt
+            ax = plt.gca()
+
+        kwargs = {'where': 'post'}
+        kwargs.update(matplotlib_kwargs)
+
+        delta = np.ptp(self.quantiles)*0.05  # how far past sample edge to plot
+        q = self.quantiles
+        q = [q[0] - delta] + list(q) + [q[-1] + delta]
+
+        return ax.step(q, self.evaluate(q), **kwargs)
+
+    def confidence_interval(self, confidence_level=0.95, *, method='linear'):
+        """Compute a confidence interval around the CDF/SF point estimate
+
+        Parameters
+        ----------
+        confidence_level : float, default: 0.95
+            Confidence level for the computed confidence interval
+
+        method : str, {"linear", "log-log"}
+            Method used to compute the confidence interval. Options are
+            "linear" for the conventional Greenwood confidence interval
+            (default)  and "log-log" for the "exponential Greenwood",
+            log-negative-log-transformed confidence interval.
+
+        Returns
+        -------
+        ci : ``ConfidenceInterval``
+            An object with attributes ``low`` and ``high``, instances of
+            `~scipy.stats._result_classes.EmpiricalDistributionFunction` that
+            represent the lower and upper bounds (respectively) of the
+            confidence interval.
+
+        Notes
+        -----
+        Confidence intervals are computed according to the Greenwood formula
+        (``method='linear'``) or the more recent "exponential Greenwood"
+        formula (``method='log-log'``) as described in [1]_. The conventional
+        Greenwood formula can result in lower confidence limits less than 0
+        and upper confidence limits greater than 1; these are clipped to the
+        unit interval. NaNs may be produced by either method; these are
+        features of the formulas.
+
+        References
+        ----------
+        .. [1] Sawyer, Stanley. "The Greenwood and Exponential Greenwood
+               Confidence Intervals in Survival Analysis."
+               https://www.math.wustl.edu/~sawyer/handouts/greenwood.pdf
+
+        """
+        message = ("Confidence interval bounds do not implement a "
+                   "`confidence_interval` method.")
+        if self._n is None:
+            raise NotImplementedError(message)
+
+        methods = {'linear': self._linear_ci,
+                   'log-log': self._loglog_ci}
+
+        message = f"`method` must be one of {set(methods)}."
+        if method.lower() not in methods:
+            raise ValueError(message)
+
+        message = "`confidence_level` must be a scalar between 0 and 1."
+        confidence_level = np.asarray(confidence_level)[()]
+        if confidence_level.shape or not (0 <= confidence_level <= 1):
+            raise ValueError(message)
+
+        method_fun = methods[method.lower()]
+        low, high = method_fun(confidence_level)
+
+        message = ("The confidence interval is undefined at some observations."
+                   " This is a feature of the mathematical formula used, not"
+                   " an error in its implementation.")
+        if np.any(np.isnan(low) | np.isnan(high)):
+            warnings.warn(message, RuntimeWarning, stacklevel=2)
+
+        low, high = np.clip(low, 0, 1), np.clip(high, 0, 1)
+        low = EmpiricalDistributionFunction(self.quantiles, low, None, None,
+                                            self._kind)
+        high = EmpiricalDistributionFunction(self.quantiles, high, None, None,
+                                             self._kind)
+        return ConfidenceInterval(low, high)
+
+    def _linear_ci(self, confidence_level):
+        sf, d, n = self._sf, self._d, self._n
+        # When n == d, Greenwood's formula divides by zero.
+        # When s != 0, this can be ignored: var == inf, and CI is [0, 1]
+        # When s == 0, this results in NaNs. Produce an informative warning.
+        with np.errstate(divide='ignore', invalid='ignore'):
+            var = sf ** 2 * np.cumsum(d / (n * (n - d)))
+
+        se = np.sqrt(var)
+        z = special.ndtri(1 / 2 + confidence_level / 2)
+
+        z_se = z * se
+        low = self.probabilities - z_se
+        high = self.probabilities + z_se
+
+        return low, high
+
+    def _loglog_ci(self, confidence_level):
+        sf, d, n = self._sf, self._d, self._n
+
+        with np.errstate(divide='ignore', invalid='ignore'):
+            var = 1 / np.log(sf) ** 2 * np.cumsum(d / (n * (n - d)))
+
+        se = np.sqrt(var)
+        z = special.ndtri(1 / 2 + confidence_level / 2)
+
+        with np.errstate(divide='ignore'):
+            lnl_points = np.log(-np.log(sf))
+
+        z_se = z * se
+        low = np.exp(-np.exp(lnl_points + z_se))
+        high = np.exp(-np.exp(lnl_points - z_se))
+        if self._kind == "cdf":
+            low, high = 1-high, 1-low
+
+        return low, high
+
+
+@dataclass
+class ECDFResult:
+    """ Result object returned by `scipy.stats.ecdf`
+
+    Attributes
+    ----------
+    cdf : `~scipy.stats._result_classes.EmpiricalDistributionFunction`
+        An object representing the empirical cumulative distribution function.
+    sf : `~scipy.stats._result_classes.EmpiricalDistributionFunction`
+        An object representing the complement of the empirical cumulative
+        distribution function.
+    """
+    cdf: EmpiricalDistributionFunction
+    sf: EmpiricalDistributionFunction
+
+    def __init__(self, q, cdf, sf, n, d):
+        self.cdf = EmpiricalDistributionFunction(q, cdf, n, d, "cdf")
+        self.sf = EmpiricalDistributionFunction(q, sf, n, d, "sf")
+
+
+def _iv_CensoredData(
+    sample: npt.ArrayLike | CensoredData, param_name: str = 'sample'
+) -> CensoredData:
+    """Attempt to convert `sample` to `CensoredData`."""
+    if not isinstance(sample, CensoredData):
+        try:  # takes care of input standardization/validation
+            sample = CensoredData(uncensored=sample)
+        except ValueError as e:
+            message = str(e).replace('uncensored', param_name)
+            raise type(e)(message) from e
+    return sample
+
+
+def ecdf(sample: npt.ArrayLike | CensoredData) -> ECDFResult:
+    """Empirical cumulative distribution function of a sample.
+
+    The empirical cumulative distribution function (ECDF) is a step function
+    estimate of the CDF of the distribution underlying a sample. This function
+    returns objects representing both the empirical distribution function and
+    its complement, the empirical survival function.
+
+    Parameters
+    ----------
+    sample : 1D array_like or `scipy.stats.CensoredData`
+        Besides array_like, instances of `scipy.stats.CensoredData` containing
+        uncensored and right-censored observations are supported. Currently,
+        other instances of `scipy.stats.CensoredData` will result in a
+        ``NotImplementedError``.
+
+    Returns
+    -------
+    res : `~scipy.stats._result_classes.ECDFResult`
+        An object with the following attributes.
+
+        cdf : `~scipy.stats._result_classes.EmpiricalDistributionFunction`
+            An object representing the empirical cumulative distribution
+            function.
+        sf : `~scipy.stats._result_classes.EmpiricalDistributionFunction`
+            An object representing the empirical survival function.
+
+        The `cdf` and `sf` attributes themselves have the following attributes.
+
+        quantiles : ndarray
+            The unique values in the sample that defines the empirical CDF/SF.
+        probabilities : ndarray
+            The point estimates of the probabilities corresponding with
+            `quantiles`.
+
+        And the following methods:
+
+        evaluate(x) :
+            Evaluate the CDF/SF at the argument.
+
+        plot(ax) :
+            Plot the CDF/SF on the provided axes.
+
+        confidence_interval(confidence_level=0.95) :
+            Compute the confidence interval around the CDF/SF at the values in
+            `quantiles`.
+
+    Notes
+    -----
+    When each observation of the sample is a precise measurement, the ECDF
+    steps up by ``1/len(sample)`` at each of the observations [1]_.
+
+    When observations are lower bounds, upper bounds, or both upper and lower
+    bounds, the data is said to be "censored", and `sample` may be provided as
+    an instance of `scipy.stats.CensoredData`.
+
+    For right-censored data, the ECDF is given by the Kaplan-Meier estimator
+    [2]_; other forms of censoring are not supported at this time.
+
+    Confidence intervals are computed according to the Greenwood formula or the
+    more recent "Exponential Greenwood" formula as described in [4]_.
+
+    References
+    ----------
+    .. [1] Conover, William Jay. Practical nonparametric statistics. Vol. 350.
+           John Wiley & Sons, 1999.
+
+    .. [2] Kaplan, Edward L., and Paul Meier. "Nonparametric estimation from
+           incomplete observations." Journal of the American statistical
+           association 53.282 (1958): 457-481.
+
+    .. [3] Goel, Manish Kumar, Pardeep Khanna, and Jugal Kishore.
+           "Understanding survival analysis: Kaplan-Meier estimate."
+           International journal of Ayurveda research 1.4 (2010): 274.
+
+    .. [4] Sawyer, Stanley. "The Greenwood and Exponential Greenwood Confidence
+           Intervals in Survival Analysis."
+           https://www.math.wustl.edu/~sawyer/handouts/greenwood.pdf
+
+    Examples
+    --------
+    **Uncensored Data**
+
+    As in the example from [1]_ page 79, five boys were selected at random from
+    those in a single high school. Their one-mile run times were recorded as
+    follows.
+
+    >>> sample = [6.23, 5.58, 7.06, 6.42, 5.20]  # one-mile run times (minutes)
+
+    The empirical distribution function, which approximates the distribution
+    function of one-mile run times of the population from which the boys were
+    sampled, is calculated as follows.
+
+    >>> from scipy import stats
+    >>> res = stats.ecdf(sample)
+    >>> res.cdf.quantiles
+    array([5.2 , 5.58, 6.23, 6.42, 7.06])
+    >>> res.cdf.probabilities
+    array([0.2, 0.4, 0.6, 0.8, 1. ])
+
+    To plot the result as a step function:
+
+    >>> import matplotlib.pyplot as plt
+    >>> ax = plt.subplot()
+    >>> res.cdf.plot(ax)
+    >>> ax.set_xlabel('One-Mile Run Time (minutes)')
+    >>> ax.set_ylabel('Empirical CDF')
+    >>> plt.show()
+
+    **Right-censored Data**
+
+    As in the example from [1]_ page 91, the lives of ten car fanbelts were
+    tested. Five tests concluded because the fanbelt being tested broke, but
+    the remaining tests concluded for other reasons (e.g. the study ran out of
+    funding, but the fanbelt was still functional). The mileage driven
+    with the fanbelts were recorded as follows.
+
+    >>> broken = [77, 47, 81, 56, 80]  # in thousands of miles driven
+    >>> unbroken = [62, 60, 43, 71, 37]
+
+    Precise survival times of the fanbelts that were still functional at the
+    end of the tests are unknown, but they are known to exceed the values
+    recorded in ``unbroken``. Therefore, these observations are said to be
+    "right-censored", and the data is represented using
+    `scipy.stats.CensoredData`.
+
+    >>> sample = stats.CensoredData(uncensored=broken, right=unbroken)
+
+    The empirical survival function is calculated as follows.
+
+    >>> res = stats.ecdf(sample)
+    >>> res.sf.quantiles
+    array([37., 43., 47., 56., 60., 62., 71., 77., 80., 81.])
+    >>> res.sf.probabilities
+    array([1.   , 1.   , 0.875, 0.75 , 0.75 , 0.75 , 0.75 , 0.5  , 0.25 , 0.   ])
+
+    To plot the result as a step function:
+
+    >>> ax = plt.subplot()
+    >>> res.cdf.plot(ax)
+    >>> ax.set_xlabel('Fanbelt Survival Time (thousands of miles)')
+    >>> ax.set_ylabel('Empirical SF')
+    >>> plt.show()
+
+    """
+    sample = _iv_CensoredData(sample)
+
+    if sample.num_censored() == 0:
+        res = _ecdf_uncensored(sample._uncensor())
+    elif sample.num_censored() == sample._right.size:
+        res = _ecdf_right_censored(sample)
+    else:
+        # Support additional censoring options in follow-up PRs
+        message = ("Currently, only uncensored and right-censored data is "
+                   "supported.")
+        raise NotImplementedError(message)
+
+    t, cdf, sf, n, d = res
+    return ECDFResult(t, cdf, sf, n, d)
+
+
+def _ecdf_uncensored(sample):
+    sample = np.sort(sample)
+    x, counts = np.unique(sample, return_counts=True)
+
+    # [1].81 "the fraction of [observations] that are less than or equal to x
+    events = np.cumsum(counts)
+    n = sample.size
+    cdf = events / n
+
+    # [1].89 "the relative frequency of the sample that exceeds x in value"
+    sf = 1 - cdf
+
+    at_risk = np.concatenate(([n], n - events[:-1]))
+    return x, cdf, sf, at_risk, counts
+
+
+def _ecdf_right_censored(sample):
+    # It is conventional to discuss right-censored data in terms of
+    # "survival time", "death", and "loss" (e.g. [2]). We'll use that
+    # terminology here.
+    # This implementation was influenced by the references cited and also
+    # https://www.youtube.com/watch?v=lxoWsVco_iM
+    # https://en.wikipedia.org/wiki/Kaplan%E2%80%93Meier_estimator
+    # In retrospect it is probably most easily compared against [3].
+    # Ultimately, the data needs to be sorted, so this implementation is
+    # written to avoid a separate call to `unique` after sorting. In hope of
+    # better performance on large datasets, it also computes survival
+    # probabilities at unique times only rather than at each observation.
+    tod = sample._uncensored  # time of "death"
+    tol = sample._right  # time of "loss"
+    times = np.concatenate((tod, tol))
+    died = np.asarray([1]*tod.size + [0]*tol.size)
+
+    # sort by times
+    i = np.argsort(times)
+    times = times[i]
+    died = died[i]
+    at_risk = np.arange(times.size, 0, -1)
+
+    # logical indices of unique times
+    j = np.diff(times, prepend=-np.inf, append=np.inf) > 0
+    j_l = j[:-1]  # first instances of unique times
+    j_r = j[1:]  # last instances of unique times
+
+    # get number at risk and deaths at each unique time
+    t = times[j_l]  # unique times
+    n = at_risk[j_l]  # number at risk at each unique time
+    cd = np.cumsum(died)[j_r]  # cumulative deaths up to/including unique times
+    d = np.diff(cd, prepend=0)  # deaths at each unique time
+
+    # compute survival function
+    sf = np.cumprod((n - d) / n)
+    cdf = 1 - sf
+    return t, cdf, sf, n, d
+
+
+@dataclass
+class LogRankResult:
+    """Result object returned by `scipy.stats.logrank`.
+
+    Attributes
+    ----------
+    statistic : float ndarray
+        The computed statistic (defined below). Its magnitude is the
+        square root of the magnitude returned by most other logrank test
+        implementations.
+    pvalue : float ndarray
+        The computed p-value of the test.
+    """
+    statistic: np.ndarray
+    pvalue: np.ndarray
+
+
+def logrank(
+    x: npt.ArrayLike | CensoredData,
+    y: npt.ArrayLike | CensoredData,
+    alternative: Literal['two-sided', 'less', 'greater'] = "two-sided"
+) -> LogRankResult:
+    r"""Compare the survival distributions of two samples via the logrank test.
+
+    Parameters
+    ----------
+    x, y : array_like or CensoredData
+        Samples to compare based on their empirical survival functions.
+    alternative : {'two-sided', 'less', 'greater'}, optional
+        Defines the alternative hypothesis.
+
+        The null hypothesis is that the survival distributions of the two
+        groups, say *X* and *Y*, are identical.
+
+        The following alternative hypotheses [4]_ are available (default is
+        'two-sided'):
+
+        * 'two-sided': the survival distributions of the two groups are not
+          identical.
+        * 'less': survival of group *X* is favored: the group *X* failure rate
+          function is less than the group *Y* failure rate function at some
+          times.
+        * 'greater': survival of group *Y* is favored: the group *X* failure
+          rate function is greater than the group *Y* failure rate function at
+          some times.
+
+    Returns
+    -------
+    res : `~scipy.stats._result_classes.LogRankResult`
+        An object containing attributes:
+
+        statistic : float ndarray
+            The computed statistic (defined below). Its magnitude is the
+            square root of the magnitude returned by most other logrank test
+            implementations.
+        pvalue : float ndarray
+            The computed p-value of the test.
+
+    See Also
+    --------
+    scipy.stats.ecdf
+
+    Notes
+    -----
+    The logrank test [1]_ compares the observed number of events to
+    the expected number of events under the null hypothesis that the two
+    samples were drawn from the same distribution. The statistic is
+
+    .. math::
+
+        Z_i = \frac{\sum_{j=1}^J(O_{i,j}-E_{i,j})}{\sqrt{\sum_{j=1}^J V_{i,j}}}
+        \rightarrow \mathcal{N}(0,1)
+
+    where
+
+    .. math::
+
+        E_{i,j} = O_j \frac{N_{i,j}}{N_j},
+        \qquad
+        V_{i,j} = E_{i,j} \left(\frac{N_j-O_j}{N_j}\right)
+        \left(\frac{N_j-N_{i,j}}{N_j-1}\right),
+
+    :math:`i` denotes the group (i.e. it may assume values :math:`x` or
+    :math:`y`, or it may be omitted to refer to the combined sample)
+    :math:`j` denotes the time (at which an event occurred),
+    :math:`N` is the number of subjects at risk just before an event occurred,
+    and :math:`O` is the observed number of events at that time.
+
+    The ``statistic`` :math:`Z_x` returned by `logrank` is the (signed) square
+    root of the statistic returned by many other implementations. Under the
+    null hypothesis, :math:`Z_x**2` is asymptotically distributed according to
+    the chi-squared distribution with one degree of freedom. Consequently,
+    :math:`Z_x` is asymptotically distributed according to the standard normal
+    distribution. The advantage of using :math:`Z_x` is that the sign
+    information (i.e. whether the observed number of events tends to be less
+    than or greater than the number expected under the null hypothesis) is
+    preserved, allowing `scipy.stats.logrank` to offer one-sided alternative
+    hypotheses.
+
+    References
+    ----------
+    .. [1] Mantel N. "Evaluation of survival data and two new rank order
+           statistics arising in its consideration."
+           Cancer Chemotherapy Reports, 50(3):163-170, PMID: 5910392, 1966
+    .. [2] Bland, Altman, "The logrank test", BMJ, 328:1073,
+           :doi:`10.1136/bmj.328.7447.1073`, 2004
+    .. [3] "Logrank test", Wikipedia,
+           https://en.wikipedia.org/wiki/Logrank_test
+    .. [4] Brown, Mark. "On the choice of variance for the log rank test."
+           Biometrika 71.1 (1984): 65-74.
+    .. [5] Klein, John P., and Melvin L. Moeschberger. Survival analysis:
+           techniques for censored and truncated data. Vol. 1230. New York:
+           Springer, 2003.
+
+    Examples
+    --------
+    Reference [2]_ compared the survival times of patients with two different
+    types of recurrent malignant gliomas. The samples below record the time
+    (number of weeks) for which each patient participated in the study. The
+    `scipy.stats.CensoredData` class is used because the data is
+    right-censored: the uncensored observations correspond with observed deaths
+    whereas the censored observations correspond with the patient leaving the
+    study for another reason.
+
+    >>> from scipy import stats
+    >>> x = stats.CensoredData(
+    ...     uncensored=[6, 13, 21, 30, 37, 38, 49, 50,
+    ...                 63, 79, 86, 98, 202, 219],
+    ...     right=[31, 47, 80, 82, 82, 149]
+    ... )
+    >>> y = stats.CensoredData(
+    ...     uncensored=[10, 10, 12, 13, 14, 15, 16, 17, 18, 20, 24, 24,
+    ...                 25, 28,30, 33, 35, 37, 40, 40, 46, 48, 76, 81,
+    ...                 82, 91, 112, 181],
+    ...     right=[34, 40, 70]
+    ... )
+
+    We can calculate and visualize the empirical survival functions
+    of both groups as follows.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> ax = plt.subplot()
+    >>> ecdf_x = stats.ecdf(x)
+    >>> ecdf_x.sf.plot(ax, label='Astrocytoma')
+    >>> ecdf_y = stats.ecdf(y)
+    >>> ecdf_y.sf.plot(ax, label='Glioblastoma')
+    >>> ax.set_xlabel('Time to death (weeks)')
+    >>> ax.set_ylabel('Empirical SF')
+    >>> plt.legend()
+    >>> plt.show()
+
+    Visual inspection of the empirical survival functions suggests that the
+    survival times tend to be different between the two groups. To formally
+    assess whether the difference is significant at the 1% level, we use the
+    logrank test.
+
+    >>> res = stats.logrank(x=x, y=y)
+    >>> res.statistic
+    -2.73799
+    >>> res.pvalue
+    0.00618
+
+    The p-value is less than 1%, so we can consider the data to be evidence
+    against the null hypothesis in favor of the alternative that there is a
+    difference between the two survival functions.
+
+    """
+    # Input validation. `alternative` IV handled in `_get_pvalue` below.
+    x = _iv_CensoredData(sample=x, param_name='x')
+    y = _iv_CensoredData(sample=y, param_name='y')
+
+    # Combined sample. (Under H0, the two groups are identical.)
+    xy = CensoredData(
+        uncensored=np.concatenate((x._uncensored, y._uncensored)),
+        right=np.concatenate((x._right, y._right))
+    )
+
+    # Extract data from the combined sample
+    res = ecdf(xy)
+    idx = res.sf._d.astype(bool)  # indices of observed events
+    times_xy = res.sf.quantiles[idx]  # unique times of observed events
+    at_risk_xy = res.sf._n[idx]  # combined number of subjects at risk
+    deaths_xy = res.sf._d[idx]  # combined number of events
+
+    # Get the number at risk within each sample.
+    # First compute the number at risk in group X at each of the `times_xy`.
+    # Could use `interpolate_1d`, but this is more compact.
+    res_x = ecdf(x)
+    i = np.searchsorted(res_x.sf.quantiles, times_xy)
+    at_risk_x = np.append(res_x.sf._n, 0)[i]  # 0 at risk after last time
+    # Subtract from the combined number at risk to get number at risk in Y
+    at_risk_y = at_risk_xy - at_risk_x
+
+    # Compute the variance.
+    num = at_risk_x * at_risk_y * deaths_xy * (at_risk_xy - deaths_xy)
+    den = at_risk_xy**2 * (at_risk_xy - 1)
+    # Note: when `at_risk_xy == 1`, we would have `at_risk_xy - 1 == 0` in the
+    # numerator and denominator. Simplifying the fraction symbolically, we
+    # would always find the overall quotient to be zero, so don't compute it.
+    i = at_risk_xy > 1
+    sum_var = np.sum(num[i]/den[i])
+
+    # Get the observed and expected number of deaths in group X
+    n_died_x = x._uncensored.size
+    sum_exp_deaths_x = np.sum(at_risk_x * (deaths_xy/at_risk_xy))
+
+    # Compute the statistic. This is the square root of that in references.
+    statistic = (n_died_x - sum_exp_deaths_x)/np.sqrt(sum_var)
+
+    # Equivalent to chi2(df=1).sf(statistic**2) when alternative='two-sided'
+    norm = stats._stats_py._SimpleNormal()
+    pvalue = stats._stats_py._get_pvalue(statistic, norm, alternative, xp=np)
+
+    return LogRankResult(statistic=statistic[()], pvalue=pvalue[()])

parrot/lib/python3.10/site-packages/scipy/stats/contingency.py

@@ -0,0 +1,468 @@
+"""
+Contingency table functions (:mod:`scipy.stats.contingency`)
+============================================================
+
+Functions for creating and analyzing contingency tables.
+
+.. currentmodule:: scipy.stats.contingency
+
+.. autosummary::
+   :toctree: generated/
+
+   chi2_contingency
+   relative_risk
+   odds_ratio
+   crosstab
+   association
+
+   expected_freq
+   margins
+
+"""
+
+
+from functools import reduce
+import math
+import numpy as np
+from ._stats_py import power_divergence
+from ._relative_risk import relative_risk
+from ._crosstab import crosstab
+from ._odds_ratio import odds_ratio
+from scipy._lib._bunch import _make_tuple_bunch
+
+
+__all__ = ['margins', 'expected_freq', 'chi2_contingency', 'crosstab',
+           'association', 'relative_risk', 'odds_ratio']
+
+
+def margins(a):
+    """Return a list of the marginal sums of the array `a`.
+
+    Parameters
+    ----------
+    a : ndarray
+        The array for which to compute the marginal sums.
+
+    Returns
+    -------
+    margsums : list of ndarrays
+        A list of length `a.ndim`.  `margsums[k]` is the result
+        of summing `a` over all axes except `k`; it has the same
+        number of dimensions as `a`, but the length of each axis
+        except axis `k` will be 1.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats.contingency import margins
+
+    >>> a = np.arange(12).reshape(2, 6)
+    >>> a
+    array([[ 0,  1,  2,  3,  4,  5],
+           [ 6,  7,  8,  9, 10, 11]])
+    >>> m0, m1 = margins(a)
+    >>> m0
+    array([[15],
+           [51]])
+    >>> m1
+    array([[ 6,  8, 10, 12, 14, 16]])
+
+    >>> b = np.arange(24).reshape(2,3,4)
+    >>> m0, m1, m2 = margins(b)
+    >>> m0
+    array([[[ 66]],
+           [[210]]])
+    >>> m1
+    array([[[ 60],
+            [ 92],
+            [124]]])
+    >>> m2
+    array([[[60, 66, 72, 78]]])
+    """
+    margsums = []
+    ranged = list(range(a.ndim))
+    for k in ranged:
+        marg = np.apply_over_axes(np.sum, a, [j for j in ranged if j != k])
+        margsums.append(marg)
+    return margsums
+
+
+def expected_freq(observed):
+    """
+    Compute the expected frequencies from a contingency table.
+
+    Given an n-dimensional contingency table of observed frequencies,
+    compute the expected frequencies for the table based on the marginal
+    sums under the assumption that the groups associated with each
+    dimension are independent.
+
+    Parameters
+    ----------
+    observed : array_like
+        The table of observed frequencies.  (While this function can handle
+        a 1-D array, that case is trivial.  Generally `observed` is at
+        least 2-D.)
+
+    Returns
+    -------
+    expected : ndarray of float64
+        The expected frequencies, based on the marginal sums of the table.
+        Same shape as `observed`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.stats.contingency import expected_freq
+    >>> observed = np.array([[10, 10, 20],[20, 20, 20]])
+    >>> expected_freq(observed)
+    array([[ 12.,  12.,  16.],
+           [ 18.,  18.,  24.]])
+
+    """
+    # Typically `observed` is an integer array. If `observed` has a large
+    # number of dimensions or holds large values, some of the following
+    # computations may overflow, so we first switch to floating point.
+    observed = np.asarray(observed, dtype=np.float64)
+
+    # Create a list of the marginal sums.
+    margsums = margins(observed)
+
+    # Create the array of expected frequencies.  The shapes of the
+    # marginal sums returned by apply_over_axes() are just what we
+    # need for broadcasting in the following product.
+    d = observed.ndim
+    expected = reduce(np.multiply, margsums) / observed.sum() ** (d - 1)
+    return expected
+
+
+Chi2ContingencyResult = _make_tuple_bunch(
+    'Chi2ContingencyResult',
+    ['statistic', 'pvalue', 'dof', 'expected_freq'], []
+)
+
+
+def chi2_contingency(observed, correction=True, lambda_=None):
+    """Chi-square test of independence of variables in a contingency table.
+
+    This function computes the chi-square statistic and p-value for the
+    hypothesis test of independence of the observed frequencies in the
+    contingency table [1]_ `observed`.  The expected frequencies are computed
+    based on the marginal sums under the assumption of independence; see
+    `scipy.stats.contingency.expected_freq`.  The number of degrees of
+    freedom is (expressed using numpy functions and attributes)::
+
+        dof = observed.size - sum(observed.shape) + observed.ndim - 1
+
+
+    Parameters
+    ----------
+    observed : array_like
+        The contingency table. The table contains the observed frequencies
+        (i.e. number of occurrences) in each category.  In the two-dimensional
+        case, the table is often described as an "R x C table".
+    correction : bool, optional
+        If True, *and* the degrees of freedom is 1, apply Yates' correction
+        for continuity.  The effect of the correction is to adjust each
+        observed value by 0.5 towards the corresponding expected value.
+    lambda_ : float or str, optional
+        By default, the statistic computed in this test is Pearson's
+        chi-squared statistic [2]_.  `lambda_` allows a statistic from the
+        Cressie-Read power divergence family [3]_ to be used instead.  See
+        `scipy.stats.power_divergence` for details.
+
+    Returns
+    -------
+    res : Chi2ContingencyResult
+        An object containing attributes:
+
+        statistic : float
+            The test statistic.
+        pvalue : float
+            The p-value of the test.
+        dof : int
+            The degrees of freedom.
+        expected_freq : ndarray, same shape as `observed`
+            The expected frequencies, based on the marginal sums of the table.
+
+    See Also
+    --------
+    scipy.stats.contingency.expected_freq
+    scipy.stats.fisher_exact
+    scipy.stats.chisquare
+    scipy.stats.power_divergence
+    scipy.stats.barnard_exact
+    scipy.stats.boschloo_exact
+
+    Notes
+    -----
+    An often quoted guideline for the validity of this calculation is that
+    the test should be used only if the observed and expected frequencies
+    in each cell are at least 5.
+
+    This is a test for the independence of different categories of a
+    population. The test is only meaningful when the dimension of
+    `observed` is two or more.  Applying the test to a one-dimensional
+    table will always result in `expected` equal to `observed` and a
+    chi-square statistic equal to 0.
+
+    This function does not handle masked arrays, because the calculation
+    does not make sense with missing values.
+
+    Like `scipy.stats.chisquare`, this function computes a chi-square
+    statistic; the convenience this function provides is to figure out the
+    expected frequencies and degrees of freedom from the given contingency
+    table. If these were already known, and if the Yates' correction was not
+    required, one could use `scipy.stats.chisquare`.  That is, if one calls::
+
+        res = chi2_contingency(obs, correction=False)
+
+    then the following is true::
+
+        (res.statistic, res.pvalue) == stats.chisquare(obs.ravel(),
+                                                       f_exp=ex.ravel(),
+                                                       ddof=obs.size - 1 - dof)
+
+    The `lambda_` argument was added in version 0.13.0 of scipy.
+
+    References
+    ----------
+    .. [1] "Contingency table",
+           https://en.wikipedia.org/wiki/Contingency_table
+    .. [2] "Pearson's chi-squared test",
+           https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test
+    .. [3] Cressie, N. and Read, T. R. C., "Multinomial Goodness-of-Fit
+           Tests", J. Royal Stat. Soc. Series B, Vol. 46, No. 3 (1984),
+           pp. 440-464.
+    .. [4] Berger, Jeffrey S. et al. "Aspirin for the Primary Prevention of
+           Cardiovascular Events in Women and Men: A Sex-Specific
+           Meta-analysis of Randomized Controlled Trials."
+           JAMA, 295(3):306-313, :doi:`10.1001/jama.295.3.306`, 2006.
+
+    Examples
+    --------
+    In [4]_, the use of aspirin to prevent cardiovascular events in women
+    and men was investigated. The study notably concluded:
+
+        ...aspirin therapy reduced the risk of a composite of
+        cardiovascular events due to its effect on reducing the risk of
+        ischemic stroke in women [...]
+
+    The article lists studies of various cardiovascular events. Let's
+    focus on the ischemic stoke in women.
+
+    The following table summarizes the results of the experiment in which
+    participants took aspirin or a placebo on a regular basis for several
+    years. Cases of ischemic stroke were recorded::
+
+                          Aspirin   Control/Placebo
+        Ischemic stroke     176           230
+        No stroke         21035         21018
+
+    Is there evidence that the aspirin reduces the risk of ischemic stroke?
+    We begin by formulating a null hypothesis :math:`H_0`:
+
+        The effect of aspirin is equivalent to that of placebo.
+
+    Let's assess the plausibility of this hypothesis with
+    a chi-square test.
+
+    >>> import numpy as np
+    >>> from scipy.stats import chi2_contingency
+    >>> table = np.array([[176, 230], [21035, 21018]])
+    >>> res = chi2_contingency(table)
+    >>> res.statistic
+    6.892569132546561
+    >>> res.pvalue
+    0.008655478161175739
+
+    Using a significance level of 5%, we would reject the null hypothesis in
+    favor of the alternative hypothesis: "the effect of aspirin
+    is not equivalent to the effect of placebo".
+    Because `scipy.stats.contingency.chi2_contingency` performs a two-sided
+    test, the alternative hypothesis does not indicate the direction of the
+    effect. We can use `stats.contingency.odds_ratio` to support the
+    conclusion that aspirin *reduces* the risk of ischemic stroke.
+
+    Below are further examples showing how larger contingency tables can be
+    tested.
+
+    A two-way example (2 x 3):
+
+    >>> obs = np.array([[10, 10, 20], [20, 20, 20]])
+    >>> res = chi2_contingency(obs)
+    >>> res.statistic
+    2.7777777777777777
+    >>> res.pvalue
+    0.24935220877729619
+    >>> res.dof
+    2
+    >>> res.expected_freq
+    array([[ 12.,  12.,  16.],
+           [ 18.,  18.,  24.]])
+
+    Perform the test using the log-likelihood ratio (i.e. the "G-test")
+    instead of Pearson's chi-squared statistic.
+
+    >>> res = chi2_contingency(obs, lambda_="log-likelihood")
+    >>> res.statistic
+    2.7688587616781319
+    >>> res.pvalue
+    0.25046668010954165
+
+    A four-way example (2 x 2 x 2 x 2):
+
+    >>> obs = np.array(
+    ...     [[[[12, 17],
+    ...        [11, 16]],
+    ...       [[11, 12],
+    ...        [15, 16]]],
+    ...      [[[23, 15],
+    ...        [30, 22]],
+    ...       [[14, 17],
+    ...        [15, 16]]]])
+    >>> res = chi2_contingency(obs)
+    >>> res.statistic
+    8.7584514426741897
+    >>> res.pvalue
+    0.64417725029295503
+    """
+    observed = np.asarray(observed)
+    if np.any(observed < 0):
+        raise ValueError("All values in `observed` must be nonnegative.")
+    if observed.size == 0:
+        raise ValueError("No data; `observed` has size 0.")
+
+    expected = expected_freq(observed)
+    if np.any(expected == 0):
+        # Include one of the positions where expected is zero in
+        # the exception message.
+        zeropos = list(zip(*np.nonzero(expected == 0)))[0]
+        raise ValueError("The internally computed table of expected "
+                         f"frequencies has a zero element at {zeropos}.")
+
+    # The degrees of freedom
+    dof = expected.size - sum(expected.shape) + expected.ndim - 1
+
+    if dof == 0:
+        # Degenerate case; this occurs when `observed` is 1D (or, more
+        # generally, when it has only one nontrivial dimension).  In this
+        # case, we also have observed == expected, so chi2 is 0.
+        chi2 = 0.0
+        p = 1.0
+    else:
+        if dof == 1 and correction:
+            # Adjust `observed` according to Yates' correction for continuity.
+            # Magnitude of correction no bigger than difference; see gh-13875
+            diff = expected - observed
+            direction = np.sign(diff)
+            magnitude = np.minimum(0.5, np.abs(diff))
+            observed = observed + magnitude * direction
+
+        chi2, p = power_divergence(observed, expected,
+                                   ddof=observed.size - 1 - dof, axis=None,
+                                   lambda_=lambda_)
+
+    return Chi2ContingencyResult(chi2, p, dof, expected)
+
+
+def association(observed, method="cramer", correction=False, lambda_=None):
+    """Calculates degree of association between two nominal variables.
+
+    The function provides the option for computing one of three measures of
+    association between two nominal variables from the data given in a 2d
+    contingency table: Tschuprow's T, Pearson's Contingency Coefficient
+    and Cramer's V.
+
+    Parameters
+    ----------
+    observed : array-like
+        The array of observed values
+    method : {"cramer", "tschuprow", "pearson"} (default = "cramer")
+        The association test statistic.
+    correction : bool, optional
+        Inherited from `scipy.stats.contingency.chi2_contingency()`
+    lambda_ : float or str, optional
+        Inherited from `scipy.stats.contingency.chi2_contingency()`
+
+    Returns
+    -------
+    statistic : float
+        Value of the test statistic
+
+    Notes
+    -----
+    Cramer's V, Tschuprow's T and Pearson's Contingency Coefficient, all
+    measure the degree to which two nominal or ordinal variables are related,
+    or the level of their association. This differs from correlation, although
+    many often mistakenly consider them equivalent. Correlation measures in
+    what way two variables are related, whereas, association measures how
+    related the variables are. As such, association does not subsume
+    independent variables, and is rather a test of independence. A value of
+    1.0 indicates perfect association, and 0.0 means the variables have no
+    association.
+
+    Both the Cramer's V and Tschuprow's T are extensions of the phi
+    coefficient.  Moreover, due to the close relationship between the
+    Cramer's V and Tschuprow's T the returned values can often be similar
+    or even equivalent.  They are likely to diverge more as the array shape
+    diverges from a 2x2.
+
+    References
+    ----------
+    .. [1] "Tschuprow's T",
+           https://en.wikipedia.org/wiki/Tschuprow's_T
+    .. [2] Tschuprow, A. A. (1939)
+           Principles of the Mathematical Theory of Correlation;
+           translated by M. Kantorowitsch. W. Hodge & Co.
+    .. [3] "Cramer's V", https://en.wikipedia.org/wiki/Cramer's_V
+    .. [4] "Nominal Association: Phi and Cramer's V",
+           http://www.people.vcu.edu/~pdattalo/702SuppRead/MeasAssoc/NominalAssoc.html
+    .. [5] Gingrich, Paul, "Association Between Variables",
+           http://uregina.ca/~gingrich/ch11a.pdf
+
+    Examples
+    --------
+    An example with a 4x2 contingency table:
+
+    >>> import numpy as np
+    >>> from scipy.stats.contingency import association
+    >>> obs4x2 = np.array([[100, 150], [203, 322], [420, 700], [320, 210]])
+
+    Pearson's contingency coefficient
+
+    >>> association(obs4x2, method="pearson")
+    0.18303298140595667
+
+    Cramer's V
+
+    >>> association(obs4x2, method="cramer")
+    0.18617813077483678
+
+    Tschuprow's T
+
+    >>> association(obs4x2, method="tschuprow")
+    0.14146478765062995
+    """
+    arr = np.asarray(observed)
+    if not np.issubdtype(arr.dtype, np.integer):
+        raise ValueError("`observed` must be an integer array.")
+
+    if len(arr.shape) != 2:
+        raise ValueError("method only accepts 2d arrays")
+
+    chi2_stat = chi2_contingency(arr, correction=correction,
+                                 lambda_=lambda_)
+
+    phi2 = chi2_stat.statistic / arr.sum()
+    n_rows, n_cols = arr.shape
+    if method == "cramer":
+        value = phi2 / min(n_cols - 1, n_rows - 1)
+    elif method == "tschuprow":
+        value = phi2 / math.sqrt((n_rows - 1) * (n_cols - 1))
+    elif method == 'pearson':
+        value = phi2 / (1 + phi2)
+    else:
+        raise ValueError("Invalid argument value: 'method' argument must "
+                         "be 'cramer', 'tschuprow', or 'pearson'")
+
+    return math.sqrt(value)

parrot/lib/python3.10/site-packages/scipy/stats/tests/common_tests.py

@@ -0,0 +1,354 @@
+import pickle
+
+import numpy as np
+import numpy.testing as npt
+from numpy.testing import assert_allclose, assert_equal
+from pytest import raises as assert_raises
+
+import numpy.ma.testutils as ma_npt
+
+from scipy._lib._util import (
+    getfullargspec_no_self as _getfullargspec, np_long
+)
+from scipy._lib._array_api import xp_assert_equal
+from scipy import stats
+
+
+def check_named_results(res, attributes, ma=False, xp=None):
+    for i, attr in enumerate(attributes):
+        if ma:
+            ma_npt.assert_equal(res[i], getattr(res, attr))
+        elif xp is not None:
+            xp_assert_equal(res[i], getattr(res, attr))
+        else:
+            npt.assert_equal(res[i], getattr(res, attr))
+
+
+def check_normalization(distfn, args, distname):
+    norm_moment = distfn.moment(0, *args)
+    npt.assert_allclose(norm_moment, 1.0)
+
+    if distname == "rv_histogram_instance":
+        atol, rtol = 1e-5, 0
+    else:
+        atol, rtol = 1e-7, 1e-7
+
+    normalization_expect = distfn.expect(lambda x: 1, args=args)
+    npt.assert_allclose(normalization_expect, 1.0, atol=atol, rtol=rtol,
+                        err_msg=distname, verbose=True)
+
+    _a, _b = distfn.support(*args)
+    normalization_cdf = distfn.cdf(_b, *args)
+    npt.assert_allclose(normalization_cdf, 1.0)
+
+
+def check_moment(distfn, arg, m, v, msg):
+    m1 = distfn.moment(1, *arg)
+    m2 = distfn.moment(2, *arg)
+    if not np.isinf(m):
+        npt.assert_almost_equal(m1, m, decimal=10,
+                                err_msg=msg + ' - 1st moment')
+    else:                     # or np.isnan(m1),
+        npt.assert_(np.isinf(m1),
+                    msg + ' - 1st moment -infinite, m1=%s' % str(m1))
+
+    if not np.isinf(v):
+        npt.assert_almost_equal(m2 - m1 * m1, v, decimal=10,
+                                err_msg=msg + ' - 2ndt moment')
+    else:                     # or np.isnan(m2),
+        npt.assert_(np.isinf(m2), msg + f' - 2nd moment -infinite, {m2=}')
+
+
+def check_mean_expect(distfn, arg, m, msg):
+    if np.isfinite(m):
+        m1 = distfn.expect(lambda x: x, arg)
+        npt.assert_almost_equal(m1, m, decimal=5,
+                                err_msg=msg + ' - 1st moment (expect)')
+
+
+def check_var_expect(distfn, arg, m, v, msg):
+    dist_looser_tolerances = {"rv_histogram_instance" , "ksone"}
+    kwargs = {'rtol': 5e-6} if msg in dist_looser_tolerances else {}
+    if np.isfinite(v):
+        m2 = distfn.expect(lambda x: x*x, arg)
+        npt.assert_allclose(m2, v + m*m, **kwargs)
+
+
+def check_skew_expect(distfn, arg, m, v, s, msg):
+    if np.isfinite(s):
+        m3e = distfn.expect(lambda x: np.power(x-m, 3), arg)
+        npt.assert_almost_equal(m3e, s * np.power(v, 1.5),
+                                decimal=5, err_msg=msg + ' - skew')
+    else:
+        npt.assert_(np.isnan(s))
+
+
+def check_kurt_expect(distfn, arg, m, v, k, msg):
+    if np.isfinite(k):
+        m4e = distfn.expect(lambda x: np.power(x-m, 4), arg)
+        npt.assert_allclose(m4e, (k + 3.) * np.power(v, 2),
+                            atol=1e-5, rtol=1e-5,
+                            err_msg=msg + ' - kurtosis')
+    elif not np.isposinf(k):
+        npt.assert_(np.isnan(k))
+
+
+def check_munp_expect(dist, args, msg):
+    # If _munp is overridden, test a higher moment. (Before gh-18634, some
+    # distributions had issues with moments 5 and higher.)
+    if dist._munp.__func__ != stats.rv_continuous._munp:
+        res = dist.moment(5, *args)  # shouldn't raise an error
+        ref = dist.expect(lambda x: x ** 5, args, lb=-np.inf, ub=np.inf)
+        if not np.isfinite(res):  # could be valid; automated test can't know
+            return
+        # loose tolerance, mostly to see whether _munp returns *something*
+        assert_allclose(res, ref, atol=1e-10, rtol=1e-4,
+                        err_msg=msg + ' - higher moment / _munp')
+
+
+def check_entropy(distfn, arg, msg):
+    ent = distfn.entropy(*arg)
+    npt.assert_(not np.isnan(ent), msg + 'test Entropy is nan')
+
+
+def check_private_entropy(distfn, args, superclass):
+    # compare a generic _entropy with the distribution-specific implementation
+    npt.assert_allclose(distfn._entropy(*args),
+                        superclass._entropy(distfn, *args))
+
+
+def check_entropy_vect_scale(distfn, arg):
+    # check 2-d
+    sc = np.asarray([[1, 2], [3, 4]])
+    v_ent = distfn.entropy(*arg, scale=sc)
+    s_ent = [distfn.entropy(*arg, scale=s) for s in sc.ravel()]
+    s_ent = np.asarray(s_ent).reshape(v_ent.shape)
+    assert_allclose(v_ent, s_ent, atol=1e-14)
+
+    # check invalid value, check cast
+    sc = [1, 2, -3]
+    v_ent = distfn.entropy(*arg, scale=sc)
+    s_ent = [distfn.entropy(*arg, scale=s) for s in sc]
+    s_ent = np.asarray(s_ent).reshape(v_ent.shape)
+    assert_allclose(v_ent, s_ent, atol=1e-14)
+
+
+def check_edge_support(distfn, args):
+    # Make sure that x=self.a and self.b are handled correctly.
+    x = distfn.support(*args)
+    if isinstance(distfn, stats.rv_discrete):
+        x = x[0]-1, x[1]
+
+    npt.assert_equal(distfn.cdf(x, *args), [0.0, 1.0])
+    npt.assert_equal(distfn.sf(x, *args), [1.0, 0.0])
+
+    if distfn.name not in ('skellam', 'dlaplace'):
+        # with a = -inf, log(0) generates warnings
+        npt.assert_equal(distfn.logcdf(x, *args), [-np.inf, 0.0])
+        npt.assert_equal(distfn.logsf(x, *args), [0.0, -np.inf])
+
+    npt.assert_equal(distfn.ppf([0.0, 1.0], *args), x)
+    npt.assert_equal(distfn.isf([0.0, 1.0], *args), x[::-1])
+
+    # out-of-bounds for isf & ppf
+    npt.assert_(np.isnan(distfn.isf([-1, 2], *args)).all())
+    npt.assert_(np.isnan(distfn.ppf([-1, 2], *args)).all())
+
+
+def check_named_args(distfn, x, shape_args, defaults, meths):
+    ## Check calling w/ named arguments.
+
+    # check consistency of shapes, numargs and _parse signature
+    signature = _getfullargspec(distfn._parse_args)
+    npt.assert_(signature.varargs is None)
+    npt.assert_(signature.varkw is None)
+    npt.assert_(not signature.kwonlyargs)
+    npt.assert_(list(signature.defaults) == list(defaults))
+
+    shape_argnames = signature.args[:-len(defaults)]  # a, b, loc=0, scale=1
+    if distfn.shapes:
+        shapes_ = distfn.shapes.replace(',', ' ').split()
+    else:
+        shapes_ = ''
+    npt.assert_(len(shapes_) == distfn.numargs)
+    npt.assert_(len(shapes_) == len(shape_argnames))
+
+    # check calling w/ named arguments
+    shape_args = list(shape_args)
+
+    vals = [meth(x, *shape_args) for meth in meths]
+    npt.assert_(np.all(np.isfinite(vals)))
+
+    names, a, k = shape_argnames[:], shape_args[:], {}
+    while names:
+        k.update({names.pop(): a.pop()})
+        v = [meth(x, *a, **k) for meth in meths]
+        npt.assert_array_equal(vals, v)
+        if 'n' not in k.keys():
+            # `n` is first parameter of moment(), so can't be used as named arg
+            npt.assert_equal(distfn.moment(1, *a, **k),
+                             distfn.moment(1, *shape_args))
+
+    # unknown arguments should not go through:
+    k.update({'kaboom': 42})
+    assert_raises(TypeError, distfn.cdf, x, **k)
+
+
+def check_random_state_property(distfn, args):
+    # check the random_state attribute of a distribution *instance*
+
+    # This test fiddles with distfn.random_state. This breaks other tests,
+    # hence need to save it and then restore.
+    rndm = distfn.random_state
+
+    # baseline: this relies on the global state
+    np.random.seed(1234)
+    distfn.random_state = None
+    r0 = distfn.rvs(*args, size=8)
+
+    # use an explicit instance-level random_state
+    distfn.random_state = 1234
+    r1 = distfn.rvs(*args, size=8)
+    npt.assert_equal(r0, r1)
+
+    distfn.random_state = np.random.RandomState(1234)
+    r2 = distfn.rvs(*args, size=8)
+    npt.assert_equal(r0, r2)
+
+    # check that np.random.Generator can be used (numpy >= 1.17)
+    if hasattr(np.random, 'default_rng'):
+        # obtain a np.random.Generator object
+        rng = np.random.default_rng(1234)
+        distfn.rvs(*args, size=1, random_state=rng)
+
+    # can override the instance-level random_state for an individual .rvs call
+    distfn.random_state = 2
+    orig_state = distfn.random_state.get_state()
+
+    r3 = distfn.rvs(*args, size=8, random_state=np.random.RandomState(1234))
+    npt.assert_equal(r0, r3)
+
+    # ... and that does not alter the instance-level random_state!
+    npt.assert_equal(distfn.random_state.get_state(), orig_state)
+
+    # finally, restore the random_state
+    distfn.random_state = rndm
+
+
+def check_meth_dtype(distfn, arg, meths):
+    q0 = [0.25, 0.5, 0.75]
+    x0 = distfn.ppf(q0, *arg)
+    x_cast = [x0.astype(tp) for tp in (np_long, np.float16, np.float32,
+                                       np.float64)]
+
+    for x in x_cast:
+        # casting may have clipped the values, exclude those
+        distfn._argcheck(*arg)
+        x = x[(distfn.a < x) & (x < distfn.b)]
+        for meth in meths:
+            val = meth(x, *arg)
+            npt.assert_(val.dtype == np.float64)
+
+
+def check_ppf_dtype(distfn, arg):
+    q0 = np.asarray([0.25, 0.5, 0.75])
+    q_cast = [q0.astype(tp) for tp in (np.float16, np.float32, np.float64)]
+    for q in q_cast:
+        for meth in [distfn.ppf, distfn.isf]:
+            val = meth(q, *arg)
+            npt.assert_(val.dtype == np.float64)
+
+
+def check_cmplx_deriv(distfn, arg):
+    # Distributions allow complex arguments.
+    def deriv(f, x, *arg):
+        x = np.asarray(x)
+        h = 1e-10
+        return (f(x + h*1j, *arg)/h).imag
+
+    x0 = distfn.ppf([0.25, 0.51, 0.75], *arg)
+    x_cast = [x0.astype(tp) for tp in (np_long, np.float16, np.float32,
+                                       np.float64)]
+
+    for x in x_cast:
+        # casting may have clipped the values, exclude those
+        distfn._argcheck(*arg)
+        x = x[(distfn.a < x) & (x < distfn.b)]
+
+        pdf, cdf, sf = distfn.pdf(x, *arg), distfn.cdf(x, *arg), distfn.sf(x, *arg)
+        assert_allclose(deriv(distfn.cdf, x, *arg), pdf, rtol=1e-5)
+        assert_allclose(deriv(distfn.logcdf, x, *arg), pdf/cdf, rtol=1e-5)
+
+        assert_allclose(deriv(distfn.sf, x, *arg), -pdf, rtol=1e-5)
+        assert_allclose(deriv(distfn.logsf, x, *arg), -pdf/sf, rtol=1e-5)
+
+        assert_allclose(deriv(distfn.logpdf, x, *arg),
+                        deriv(distfn.pdf, x, *arg) / distfn.pdf(x, *arg),
+                        rtol=1e-5)
+
+
+def check_pickling(distfn, args):
+    # check that a distribution instance pickles and unpickles
+    # pay special attention to the random_state property
+
+    # save the random_state (restore later)
+    rndm = distfn.random_state
+
+    # check unfrozen
+    distfn.random_state = 1234
+    distfn.rvs(*args, size=8)
+    s = pickle.dumps(distfn)
+    r0 = distfn.rvs(*args, size=8)
+
+    unpickled = pickle.loads(s)
+    r1 = unpickled.rvs(*args, size=8)
+    npt.assert_equal(r0, r1)
+
+    # also smoke test some methods
+    medians = [distfn.ppf(0.5, *args), unpickled.ppf(0.5, *args)]
+    npt.assert_equal(medians[0], medians[1])
+    npt.assert_equal(distfn.cdf(medians[0], *args),
+                     unpickled.cdf(medians[1], *args))
+
+    # check frozen pickling/unpickling with rvs
+    frozen_dist = distfn(*args)
+    pkl = pickle.dumps(frozen_dist)
+    unpickled = pickle.loads(pkl)
+
+    r0 = frozen_dist.rvs(size=8)
+    r1 = unpickled.rvs(size=8)
+    npt.assert_equal(r0, r1)
+
+    # check pickling/unpickling of .fit method
+    if hasattr(distfn, "fit"):
+        fit_function = distfn.fit
+        pickled_fit_function = pickle.dumps(fit_function)
+        unpickled_fit_function = pickle.loads(pickled_fit_function)
+        assert fit_function.__name__ == unpickled_fit_function.__name__ == "fit"
+
+    # restore the random_state
+    distfn.random_state = rndm
+
+
+def check_freezing(distfn, args):
+    # regression test for gh-11089: freezing a distribution fails
+    # if loc and/or scale are specified
+    if isinstance(distfn, stats.rv_continuous):
+        locscale = {'loc': 1, 'scale': 2}
+    else:
+        locscale = {'loc': 1}
+
+    rv = distfn(*args, **locscale)
+    assert rv.a == distfn(*args).a
+    assert rv.b == distfn(*args).b
+
+
+def check_rvs_broadcast(distfunc, distname, allargs, shape, shape_only, otype):
+    np.random.seed(123)
+    sample = distfunc.rvs(*allargs)
+    assert_equal(sample.shape, shape, "%s: rvs failed to broadcast" % distname)
+    if not shape_only:
+        rvs = np.vectorize(lambda *allargs: distfunc.rvs(*allargs), otypes=otype)
+        np.random.seed(123)
+        expected = rvs(*allargs)
+        assert_allclose(sample, expected, rtol=1e-13)

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_axis_nan_policy.py

@@ -0,0 +1,1290 @@
+# Many scipy.stats functions support `axis` and `nan_policy` parameters.
+# When the two are combined, it can be tricky to get all the behavior just
+# right. This file contains a suite of common tests for scipy.stats functions
+# that support `axis` and `nan_policy` and additional tests for some associated
+# functions in stats._util.
+
+from itertools import product, combinations_with_replacement, permutations
+import os
+import re
+import pickle
+import pytest
+import warnings
+
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+from scipy import stats
+from scipy.stats import norm  # type: ignore[attr-defined]
+from scipy.stats._axis_nan_policy import (_masked_arrays_2_sentinel_arrays,
+                                          SmallSampleWarning,
+                                          too_small_nd_omit, too_small_nd_not_omit,
+                                          too_small_1d_omit, too_small_1d_not_omit)
+from scipy._lib._util import AxisError
+from scipy.conftest import skip_xp_invalid_arg
+
+
+SCIPY_XSLOW = int(os.environ.get('SCIPY_XSLOW', '0'))
+
+
+def unpack_ttest_result(res):
+    low, high = res.confidence_interval()
+    return (res.statistic, res.pvalue, res.df, res._standard_error,
+            res._estimate, low, high)
+
+
+def _get_ttest_ci(ttest):
+    # get a function that returns the CI bounds of provided `ttest`
+    def ttest_ci(*args, **kwargs):
+        res = ttest(*args, **kwargs)
+        return res.confidence_interval()
+    return ttest_ci
+
+
+axis_nan_policy_cases = [
+    # function, args, kwds, number of samples, number of outputs,
+    # ... paired, unpacker function
+    # args, kwds typically aren't needed; just showing that they work
+    (stats.kruskal, tuple(), dict(), 3, 2, False, None),  # 4 samples is slow
+    (stats.ranksums, ('less',), dict(), 2, 2, False, None),
+    (stats.mannwhitneyu, tuple(), {'method': 'asymptotic'}, 2, 2, False, None),
+    (stats.wilcoxon, ('pratt',), {'mode': 'auto'}, 2, 2, True,
+     lambda res: (res.statistic, res.pvalue)),
+    (stats.wilcoxon, tuple(), dict(), 1, 2, True,
+     lambda res: (res.statistic, res.pvalue)),
+    (stats.wilcoxon, tuple(), {'mode': 'approx'}, 1, 3, True,
+     lambda res: (res.statistic, res.pvalue, res.zstatistic)),
+    (stats.gmean, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.hmean, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.pmean, (1.42,), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.sem, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.iqr, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.kurtosis, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.skew, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.kstat, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.kstatvar, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.moment, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.moment, tuple(), dict(order=[1, 2]), 1, 2, False, None),
+    (stats.jarque_bera, tuple(), dict(), 1, 2, False, None),
+    (stats.ttest_1samp, (np.array([0]),), dict(), 1, 7, False,
+     unpack_ttest_result),
+    (stats.ttest_rel, tuple(), dict(), 2, 7, True, unpack_ttest_result),
+    (stats.ttest_ind, tuple(), dict(), 2, 7, False, unpack_ttest_result),
+    (_get_ttest_ci(stats.ttest_1samp), (0,), dict(), 1, 2, False, None),
+    (_get_ttest_ci(stats.ttest_rel), tuple(), dict(), 2, 2, True, None),
+    (_get_ttest_ci(stats.ttest_ind), tuple(), dict(), 2, 2, False, None),
+    (stats.mode, tuple(), dict(), 1, 2, True, lambda x: (x.mode, x.count)),
+    (stats.differential_entropy, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.variation, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.friedmanchisquare, tuple(), dict(), 3, 2, True, None),
+    (stats.brunnermunzel, tuple(), dict(distribution='normal'), 2, 2, False, None),
+    (stats.mood, tuple(), {}, 2, 2, False, None),
+    (stats.shapiro, tuple(), {}, 1, 2, False, None),
+    (stats.ks_1samp, (norm().cdf,), dict(), 1, 4, False,
+     lambda res: (*res, res.statistic_location, res.statistic_sign)),
+    (stats.ks_2samp, tuple(), dict(), 2, 4, False,
+     lambda res: (*res, res.statistic_location, res.statistic_sign)),
+    (stats.kstest, (norm().cdf,), dict(), 1, 4, False,
+     lambda res: (*res, res.statistic_location, res.statistic_sign)),
+    (stats.kstest, tuple(), dict(), 2, 4, False,
+     lambda res: (*res, res.statistic_location, res.statistic_sign)),
+    (stats.levene, tuple(), {}, 2, 2, False, None),
+    (stats.fligner, tuple(), {'center': 'trimmed', 'proportiontocut': 0.01},
+     2, 2, False, None),
+    (stats.ansari, tuple(), {}, 2, 2, False, None),
+    (stats.entropy, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.entropy, tuple(), dict(), 2, 1, True, lambda x: (x,)),
+    (stats.skewtest, tuple(), dict(), 1, 2, False, None),
+    (stats.kurtosistest, tuple(), dict(), 1, 2, False, None),
+    (stats.normaltest, tuple(), dict(), 1, 2, False, None),
+    (stats.cramervonmises, ("norm",), dict(), 1, 2, False,
+     lambda res: (res.statistic, res.pvalue)),
+    (stats.cramervonmises_2samp, tuple(), dict(), 2, 2, False,
+     lambda res: (res.statistic, res.pvalue)),
+    (stats.epps_singleton_2samp, tuple(), dict(), 2, 2, False, None),
+    (stats.bartlett, tuple(), {}, 2, 2, False, None),
+    (stats.tmean, tuple(), {}, 1, 1, False, lambda x: (x,)),
+    (stats.tvar, tuple(), {}, 1, 1, False, lambda x: (x,)),
+    (stats.tmin, tuple(), {}, 1, 1, False, lambda x: (x,)),
+    (stats.tmax, tuple(), {}, 1, 1, False, lambda x: (x,)),
+    (stats.tstd, tuple(), {}, 1, 1, False, lambda x: (x,)),
+    (stats.tsem, tuple(), {}, 1, 1, False, lambda x: (x,)),
+    (stats.circmean, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.circvar, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.circstd, tuple(), dict(), 1, 1, False, lambda x: (x,)),
+    (stats.f_oneway, tuple(), {}, 2, 2, False, None),
+    (stats.alexandergovern, tuple(), {}, 2, 2, False,
+     lambda res: (res.statistic, res.pvalue)),
+    (stats.combine_pvalues, tuple(), {}, 1, 2, False, None),
+]
+
+# If the message is one of those expected, put nans in
+# appropriate places of `statistics` and `pvalues`
+too_small_messages = {"Degrees of freedom <= 0 for slice",
+                      "x and y should have at least 5 elements",
+                      "Data must be at least length 3",
+                      "The sample must contain at least two",
+                      "x and y must contain at least two",
+                      "division by zero",
+                      "Mean of empty slice",
+                      "Data passed to ks_2samp must not be empty",
+                      "Not enough test observations",
+                      "Not enough other observations",
+                      "Not enough observations.",
+                      "At least one observation is required",
+                      "zero-size array to reduction operation maximum",
+                      "`x` and `y` must be of nonzero size.",
+                      "The exact distribution of the Wilcoxon test",
+                      "Data input must not be empty",
+                      "Window length (0) must be positive and less",
+                      "Window length (1) must be positive and less",
+                      "Window length (2) must be positive and less",
+                      "`skewtest` requires at least",
+                      "`kurtosistest` requires at least",
+                      "attempt to get argmax of an empty sequence",
+                      "No array values within given limits",
+                      "Input sample size must be greater than one.",
+                      "invalid value encountered",
+                      "divide by zero encountered",}
+
+# If the message is one of these, results of the function may be inaccurate,
+# but NaNs are not to be placed
+inaccuracy_messages = {"Precision loss occurred in moment calculation",
+                       "Sample size too small for normal approximation."}
+
+# For some functions, nan_policy='propagate' should not just return NaNs
+override_propagate_funcs = {stats.mode}
+
+# For some functions, empty arrays produce non-NaN results
+empty_special_case_funcs = {stats.entropy}
+
+# Some functions don't follow the usual "too small" warning rules
+too_small_special_case_funcs = {stats.entropy}
+
+def _mixed_data_generator(n_samples, n_repetitions, axis, rng,
+                          paired=False):
+    # generate random samples to check the response of hypothesis tests to
+    # samples with different (but broadcastable) shapes and various
+    # nan patterns (e.g. all nans, some nans, no nans) along axis-slices
+
+    data = []
+    for i in range(n_samples):
+        n_patterns = 6  # number of distinct nan patterns
+        n_obs = 20 if paired else 20 + i  # observations per axis-slice
+        x = np.ones((n_repetitions, n_patterns, n_obs)) * np.nan
+
+        for j in range(n_repetitions):
+            samples = x[j, :, :]
+
+            # case 0: axis-slice with all nans (0 reals)
+            # cases 1-3: axis-slice with 1-3 reals (the rest nans)
+            # case 4: axis-slice with mostly (all but two) reals
+            # case 5: axis slice with all reals
+            for k, n_reals in enumerate([0, 1, 2, 3, n_obs-2, n_obs]):
+                # for cases 1-3, need paired nansw  to be in the same place
+                indices = rng.permutation(n_obs)[:n_reals]
+                samples[k, indices] = rng.random(size=n_reals)
+
+            # permute the axis-slices just to show that order doesn't matter
+            samples[:] = rng.permutation(samples, axis=0)
+
+        # For multi-sample tests, we want to test broadcasting and check
+        # that nan policy works correctly for each nan pattern for each input.
+        # This takes care of both simultaneously.
+        new_shape = [n_repetitions] + [1]*n_samples + [n_obs]
+        new_shape[1 + i] = 6
+        x = x.reshape(new_shape)
+
+        x = np.moveaxis(x, -1, axis)
+        data.append(x)
+    return data
+
+
+def _homogeneous_data_generator(n_samples, n_repetitions, axis, rng,
+                                paired=False, all_nans=True):
+    # generate random samples to check the response of hypothesis tests to
+    # samples with different (but broadcastable) shapes and homogeneous
+    # data (all nans or all finite)
+    data = []
+    for i in range(n_samples):
+        n_obs = 20 if paired else 20 + i  # observations per axis-slice
+        shape = [n_repetitions] + [1]*n_samples + [n_obs]
+        shape[1 + i] = 2
+        x = np.ones(shape) * np.nan if all_nans else rng.random(shape)
+        x = np.moveaxis(x, -1, axis)
+        data.append(x)
+    return data
+
+
+def nan_policy_1d(hypotest, data1d, unpacker, *args, n_outputs=2,
+                  nan_policy='raise', paired=False, _no_deco=True, **kwds):
+    # Reference implementation for how `nan_policy` should work for 1d samples
+
+    if nan_policy == 'raise':
+        for sample in data1d:
+            if np.any(np.isnan(sample)):
+                raise ValueError("The input contains nan values")
+
+    elif (nan_policy == 'propagate'
+          and hypotest not in override_propagate_funcs):
+        # For all hypothesis tests tested, returning nans is the right thing.
+        # But many hypothesis tests don't propagate correctly (e.g. they treat
+        # np.nan the same as np.inf, which doesn't make sense when ranks are
+        # involved) so override that behavior here.
+        for sample in data1d:
+            if np.any(np.isnan(sample)):
+                return np.full(n_outputs, np.nan)
+
+    elif nan_policy == 'omit':
+        # manually omit nans (or pairs in which at least one element is nan)
+        if not paired:
+            data1d = [sample[~np.isnan(sample)] for sample in data1d]
+        else:
+            nan_mask = np.isnan(data1d[0])
+            for sample in data1d[1:]:
+                nan_mask = np.logical_or(nan_mask, np.isnan(sample))
+            data1d = [sample[~nan_mask] for sample in data1d]
+
+    return unpacker(hypotest(*data1d, *args, _no_deco=_no_deco, **kwds))
+
+
+# These three warnings are intentional
+# For `wilcoxon` when the sample size < 50
+@pytest.mark.filterwarnings('ignore:Sample size too small for normal:UserWarning')
+# `kurtosistest` and `normaltest` when sample size < 20
+@pytest.mark.filterwarnings('ignore:`kurtosistest` p-value may be:UserWarning')
+# `foneway`
+@pytest.mark.filterwarnings('ignore:all input arrays have length 1.:RuntimeWarning')
+
+# The rest of these may or may not be desirable. They need further investigation
+# to determine whether the function's decorator should define `too_small.
+# `bartlett`, `tvar`, `tstd`, `tsem`
+@pytest.mark.filterwarnings('ignore:Degrees of freedom <= 0 for slice:RuntimeWarning')
+# kstat, kstatvar, ttest_1samp, ttest_rel, ttest_ind, ttest_ci, brunnermunzel
+# mood, levene, fligner, bartlett
+@pytest.mark.filterwarnings('ignore:Invalid value encountered in:RuntimeWarning')
+# kstatvar, ttest_1samp, ttest_rel, ttest_ci, brunnermunzel, levene, bartlett
+@pytest.mark.filterwarnings('ignore:divide by zero encountered:RuntimeWarning')
+
+@pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "n_outputs",
+                          "paired", "unpacker"), axis_nan_policy_cases)
+@pytest.mark.parametrize(("nan_policy"), ("propagate", "omit", "raise"))
+@pytest.mark.parametrize(("axis"), (1,))
+@pytest.mark.parametrize(("data_generator"), ("mixed",))
+def test_axis_nan_policy_fast(hypotest, args, kwds, n_samples, n_outputs,
+                              paired, unpacker, nan_policy, axis,
+                              data_generator):
+    if hypotest in {stats.cramervonmises_2samp, stats.kruskal} and not SCIPY_XSLOW:
+        pytest.skip("Too slow.")
+    _axis_nan_policy_test(hypotest, args, kwds, n_samples, n_outputs, paired,
+                          unpacker, nan_policy, axis, data_generator)
+
+
+if SCIPY_XSLOW:
+    # Takes O(1 min) to run, and even skipping with the `xslow` decorator takes
+    # about 3 sec because this is >3,000 tests. So ensure pytest doesn't see
+    # them at all unless `SCIPY_XSLOW` is defined.
+
+    # These three warnings are intentional
+    # For `wilcoxon` when the sample size < 50
+    @pytest.mark.filterwarnings('ignore:Sample size too small for normal:UserWarning')
+    # `kurtosistest` and `normaltest` when sample size < 20
+    @pytest.mark.filterwarnings('ignore:`kurtosistest` p-value may be:UserWarning')
+    # `foneway`
+    @pytest.mark.filterwarnings('ignore:all input arrays have length 1.:RuntimeWarning')
+
+    # The rest of these may or may not be desirable. They need further investigation
+    # to determine whether the function's decorator should define `too_small.
+    # `bartlett`, `tvar`, `tstd`, `tsem`
+    @pytest.mark.filterwarnings('ignore:Degrees of freedom <= 0 for:RuntimeWarning')
+    # kstat, kstatvar, ttest_1samp, ttest_rel, ttest_ind, ttest_ci, brunnermunzel
+    # mood, levene, fligner, bartlett
+    @pytest.mark.filterwarnings('ignore:Invalid value encountered in:RuntimeWarning')
+    # kstatvar, ttest_1samp, ttest_rel, ttest_ci, brunnermunzel, levene, bartlett
+    @pytest.mark.filterwarnings('ignore:divide by zero encountered:RuntimeWarning')
+
+    @pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "n_outputs",
+                              "paired", "unpacker"), axis_nan_policy_cases)
+    @pytest.mark.parametrize(("nan_policy"), ("propagate", "omit", "raise"))
+    @pytest.mark.parametrize(("axis"), range(-3, 3))
+    @pytest.mark.parametrize(("data_generator"),
+                             ("all_nans", "all_finite", "mixed"))
+    def test_axis_nan_policy_full(hypotest, args, kwds, n_samples, n_outputs,
+                                  paired, unpacker, nan_policy, axis,
+                                  data_generator):
+        _axis_nan_policy_test(hypotest, args, kwds, n_samples, n_outputs, paired,
+                              unpacker, nan_policy, axis, data_generator)
+
+
+def _axis_nan_policy_test(hypotest, args, kwds, n_samples, n_outputs, paired,
+                          unpacker, nan_policy, axis, data_generator):
+    # Tests the 1D and vectorized behavior of hypothesis tests against a
+    # reference implementation (nan_policy_1d with np.ndenumerate)
+
+    # Some hypothesis tests return a non-iterable that needs an `unpacker` to
+    # extract the statistic and p-value. For those that don't:
+    if not unpacker:
+        def unpacker(res):
+            return res
+
+    rng = np.random.default_rng(0)
+
+    # Generate multi-dimensional test data with all important combinations
+    # of patterns of nans along `axis`
+    n_repetitions = 3  # number of repetitions of each pattern
+    data_gen_kwds = {'n_samples': n_samples, 'n_repetitions': n_repetitions,
+                     'axis': axis, 'rng': rng, 'paired': paired}
+    if data_generator == 'mixed':
+        inherent_size = 6  # number of distinct types of patterns
+        data = _mixed_data_generator(**data_gen_kwds)
+    elif data_generator == 'all_nans':
+        inherent_size = 2  # hard-coded in _homogeneous_data_generator
+        data_gen_kwds['all_nans'] = True
+        data = _homogeneous_data_generator(**data_gen_kwds)
+    elif data_generator == 'all_finite':
+        inherent_size = 2  # hard-coded in _homogeneous_data_generator
+        data_gen_kwds['all_nans'] = False
+        data = _homogeneous_data_generator(**data_gen_kwds)
+
+    output_shape = [n_repetitions] + [inherent_size]*n_samples
+
+    # To generate reference behavior to compare against, loop over the axis-
+    # slices in data. Make indexing easier by moving `axis` to the end and
+    # broadcasting all samples to the same shape.
+    data_b = [np.moveaxis(sample, axis, -1) for sample in data]
+    data_b = [np.broadcast_to(sample, output_shape + [sample.shape[-1]])
+              for sample in data_b]
+    res_1d = np.zeros(output_shape + [n_outputs])
+
+    for i, _ in np.ndenumerate(np.zeros(output_shape)):
+        data1d = [sample[i] for sample in data_b]
+        contains_nan = any([np.isnan(sample).any() for sample in data1d])
+
+        # Take care of `nan_policy='raise'`.
+        # Afterward, the 1D part of the test is over
+        message = "The input contains nan values"
+        if nan_policy == 'raise' and contains_nan:
+            with pytest.raises(ValueError, match=message):
+                nan_policy_1d(hypotest, data1d, unpacker, *args,
+                              n_outputs=n_outputs,
+                              nan_policy=nan_policy,
+                              paired=paired, _no_deco=True, **kwds)
+
+            with pytest.raises(ValueError, match=message):
+                hypotest(*data1d, *args, nan_policy=nan_policy, **kwds)
+
+            continue
+
+        # Take care of `nan_policy='propagate'` and `nan_policy='omit'`
+
+        # Get results of simple reference implementation
+        try:
+            res_1da = nan_policy_1d(hypotest, data1d, unpacker, *args,
+                                    n_outputs=n_outputs,
+                                    nan_policy=nan_policy,
+                                    paired=paired, _no_deco=True, **kwds)
+        except (ValueError, RuntimeWarning, ZeroDivisionError) as ea:
+            ea_str = str(ea)
+            if any([str(ea_str).startswith(msg) for msg in too_small_messages]):
+                res_1da = np.full(n_outputs, np.nan)
+            else:
+                raise
+
+        # Get results of public function with 1D slices
+        # Should warn for all slices
+        if (nan_policy == 'omit' and data_generator == "all_nans"
+              and hypotest not in too_small_special_case_funcs):
+            with pytest.warns(SmallSampleWarning, match=too_small_1d_omit):
+                res = hypotest(*data1d, *args, nan_policy=nan_policy, **kwds)
+        # warning depends on slice
+        elif (nan_policy == 'omit' and data_generator == "mixed"
+              and hypotest not in too_small_special_case_funcs):
+            with np.testing.suppress_warnings() as sup:
+                sup.filter(SmallSampleWarning, too_small_1d_omit)
+                res = hypotest(*data1d, *args, nan_policy=nan_policy, **kwds)
+        # shouldn't complain if there are no NaNs
+        else:
+            res = hypotest(*data1d, *args, nan_policy=nan_policy, **kwds)
+        res_1db = unpacker(res)
+
+        assert_equal(res_1db, res_1da)
+        res_1d[i] = res_1db
+
+    res_1d = np.moveaxis(res_1d, -1, 0)
+
+    # Perform a vectorized call to the hypothesis test.
+
+    # If `nan_policy == 'raise'`, check that it raises the appropriate error.
+    # Test is done, so return
+    if nan_policy == 'raise' and not data_generator == "all_finite":
+        message = 'The input contains nan values'
+        with pytest.raises(ValueError, match=message):
+            hypotest(*data, axis=axis, nan_policy=nan_policy, *args, **kwds)
+        return
+
+    # If `nan_policy == 'omit', we might be left with a small sample.
+    # Check for the appropriate warning.
+    if (nan_policy == 'omit' and data_generator in {"all_nans", "mixed"}
+          and hypotest not in too_small_special_case_funcs):
+        with pytest.warns(SmallSampleWarning, match=too_small_nd_omit):
+            res = hypotest(*data, axis=axis, nan_policy=nan_policy, *args, **kwds)
+    else:  # otherwise, there should be no warning
+        res = hypotest(*data, axis=axis, nan_policy=nan_policy, *args, **kwds)
+
+    # Compare against the output against looping over 1D slices
+    res_nd = unpacker(res)
+
+    assert_allclose(res_nd, res_1d, rtol=1e-14)
+
+
+@pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "n_outputs",
+                          "paired", "unpacker"), axis_nan_policy_cases)
+@pytest.mark.parametrize(("nan_policy"), ("propagate", "omit", "raise"))
+@pytest.mark.parametrize(("data_generator"),
+                         ("all_nans", "all_finite", "mixed", "empty"))
+def test_axis_nan_policy_axis_is_None(hypotest, args, kwds, n_samples,
+                                      n_outputs, paired, unpacker, nan_policy,
+                                      data_generator):
+    # check for correct behavior when `axis=None`
+    if not unpacker:
+        def unpacker(res):
+            return res
+
+    rng = np.random.default_rng(0)
+
+    if data_generator == "empty":
+        data = [rng.random((2, 0)) for i in range(n_samples)]
+    else:
+        data = [rng.random((2, 20)) for i in range(n_samples)]
+
+    if data_generator == "mixed":
+        masks = [rng.random((2, 20)) > 0.9 for i in range(n_samples)]
+        for sample, mask in zip(data, masks):
+            sample[mask] = np.nan
+    elif data_generator == "all_nans":
+        data = [sample * np.nan for sample in data]
+
+    data_raveled = [sample.ravel() for sample in data]
+
+    if nan_policy == 'raise' and data_generator not in {"all_finite", "empty"}:
+        message = 'The input contains nan values'
+
+        # check for correct behavior whether or not data is 1d to begin with
+        with pytest.raises(ValueError, match=message):
+            hypotest(*data, axis=None, nan_policy=nan_policy,
+                     *args, **kwds)
+        with pytest.raises(ValueError, match=message):
+            hypotest(*data_raveled, axis=None, nan_policy=nan_policy,
+                     *args, **kwds)
+
+        return
+
+    # behavior of reference implementation with 1d input, public function with 1d
+    # input, and public function with Nd input and `axis=None` should be consistent.
+    # This means:
+    # - If the reference version raises an error or emits a warning, it's because
+    #   the sample is too small, so check that the public function emits an
+    #   appropriate "too small" warning
+    # - Any results returned by the three versions should be the same.
+    with warnings.catch_warnings():  # treat warnings as errors
+        warnings.simplefilter("error")
+
+        ea_str, eb_str, ec_str = None, None, None
+        try:
+            res1da = nan_policy_1d(hypotest, data_raveled, unpacker, *args,
+                                   n_outputs=n_outputs, nan_policy=nan_policy,
+                                   paired=paired, _no_deco=True, **kwds)
+        except (RuntimeWarning, ValueError, ZeroDivisionError) as ea:
+            res1da = None
+            ea_str = str(ea)
+
+        try:
+            res1db = hypotest(*data_raveled, *args, nan_policy=nan_policy, **kwds)
+        except SmallSampleWarning as eb:
+            eb_str = str(eb)
+
+        try:
+            res1dc = hypotest(*data, *args, axis=None, nan_policy=nan_policy, **kwds)
+        except SmallSampleWarning as ec:
+            ec_str = str(ec)
+
+    if ea_str or eb_str or ec_str:  # *if* there is some sort of error or warning
+        # If the reference implemented generated an error or warning, make sure the
+        # message was one of the expected "too small" messages. Note that some
+        # functions don't complain at all without the decorator; that's OK, too.
+        ok_msg = any([str(ea_str).startswith(msg) for msg in too_small_messages])
+        assert (ea_str is None) or ok_msg
+
+        # make sure the wrapped function emits the *intended* warning
+        desired_warnings = {too_small_1d_omit, too_small_1d_not_omit}
+        assert str(eb_str) in desired_warnings
+        assert str(ec_str) in desired_warnings
+
+        with warnings.catch_warnings():  # ignore warnings to get return value
+            warnings.simplefilter("ignore")
+            res1db = hypotest(*data_raveled, *args, nan_policy=nan_policy, **kwds)
+            res1dc = hypotest(*data, *args, axis=None, nan_policy=nan_policy, **kwds)
+
+    # Make sure any results returned by reference/public function are identical
+    # and all attributes are *NumPy* scalars
+    res1db, res1dc = unpacker(res1db), unpacker(res1dc)
+    assert_equal(res1dc, res1db)
+    all_results = list(res1db) + list(res1dc)
+
+    if res1da is not None:
+        assert_equal(res1db, res1da)
+        all_results += list(res1da)
+
+    for item in all_results:
+        assert np.issubdtype(item.dtype, np.number)
+        assert np.isscalar(item)
+
+
+# Test keepdims for:
+#     - single-output and multi-output functions (gmean and mannwhitneyu)
+#     - Axis negative, positive, None, and tuple
+#     - 1D with no NaNs
+#     - 1D with NaN propagation
+#     - Zero-sized output
+@pytest.mark.filterwarnings('ignore:All axis-slices of one...')
+@pytest.mark.filterwarnings('ignore:After omitting NaNs...')
+# These were added in gh-20734 for `ttest_1samp`; they should be addressed and removed
+@pytest.mark.filterwarnings('ignore:divide by zero encountered...')
+@pytest.mark.filterwarnings('ignore:invalid value encountered...')
+@pytest.mark.parametrize("nan_policy", ("omit", "propagate"))
+@pytest.mark.parametrize(
+    ("hypotest", "args", "kwds", "n_samples", "unpacker"),
+    ((stats.gmean, tuple(), dict(), 1, lambda x: (x,)),
+     (stats.mannwhitneyu, tuple(), {'method': 'asymptotic'}, 2, None),
+     (stats.ttest_1samp, (0,), dict(), 1, unpack_ttest_result))
+)
+@pytest.mark.parametrize(
+    ("sample_shape", "axis_cases"),
+    (((2, 3, 3, 4), (None, 0, -1, (0, 2), (1, -1), (3, 1, 2, 0))),
+     ((10, ), (0, -1)),
+     ((20, 0), (0, 1)))
+)
+def test_keepdims(hypotest, args, kwds, n_samples, unpacker,
+                  sample_shape, axis_cases, nan_policy):
+    # test if keepdims parameter works correctly
+    if not unpacker:
+        def unpacker(res):
+            return res
+    rng = np.random.default_rng(0)
+    data = [rng.random(sample_shape) for _ in range(n_samples)]
+    nan_data = [sample.copy() for sample in data]
+    nan_mask = [rng.random(sample_shape) < 0.2 for _ in range(n_samples)]
+    for sample, mask in zip(nan_data, nan_mask):
+        sample[mask] = np.nan
+    for axis in axis_cases:
+        expected_shape = list(sample_shape)
+        if axis is None:
+            expected_shape = np.ones(len(sample_shape))
+        else:
+            if isinstance(axis, int):
+                expected_shape[axis] = 1
+            else:
+                for ax in axis:
+                    expected_shape[ax] = 1
+        expected_shape = tuple(expected_shape)
+        res = unpacker(hypotest(*data, *args, axis=axis, keepdims=True,
+                                **kwds))
+        res_base = unpacker(hypotest(*data, *args, axis=axis, keepdims=False,
+                                     **kwds))
+        nan_res = unpacker(hypotest(*nan_data, *args, axis=axis,
+                                    keepdims=True, nan_policy=nan_policy,
+                                    **kwds))
+        nan_res_base = unpacker(hypotest(*nan_data, *args, axis=axis,
+                                         keepdims=False,
+                                         nan_policy=nan_policy, **kwds))
+        for r, r_base, rn, rn_base in zip(res, res_base, nan_res,
+                                          nan_res_base):
+            assert r.shape == expected_shape
+            r = np.squeeze(r, axis=axis)
+            assert_equal(r, r_base)
+            assert rn.shape == expected_shape
+            rn = np.squeeze(rn, axis=axis)
+            assert_equal(rn, rn_base)
+
+
+@pytest.mark.parametrize(("fun", "nsamp"),
+                         [(stats.kstat, 1),
+                          (stats.kstatvar, 1)])
+def test_hypotest_back_compat_no_axis(fun, nsamp):
+    m, n = 8, 9
+
+    rng = np.random.default_rng(0)
+    x = rng.random((nsamp, m, n))
+    res = fun(*x)
+    res2 = fun(*x, _no_deco=True)
+    res3 = fun([xi.ravel() for xi in x])
+    assert_equal(res, res2)
+    assert_equal(res, res3)
+
+
+@pytest.mark.parametrize(("axis"), (0, 1, 2))
+def test_axis_nan_policy_decorated_positional_axis(axis):
+    # Test for correct behavior of function decorated with
+    # _axis_nan_policy_decorator whether `axis` is provided as positional or
+    # keyword argument
+
+    shape = (8, 9, 10)
+    rng = np.random.default_rng(0)
+    x = rng.random(shape)
+    y = rng.random(shape)
+    res1 = stats.mannwhitneyu(x, y, True, 'two-sided', axis)
+    res2 = stats.mannwhitneyu(x, y, True, 'two-sided', axis=axis)
+    assert_equal(res1, res2)
+
+    message = "mannwhitneyu() got multiple values for argument 'axis'"
+    with pytest.raises(TypeError, match=re.escape(message)):
+        stats.mannwhitneyu(x, y, True, 'two-sided', axis, axis=axis)
+
+
+def test_axis_nan_policy_decorated_positional_args():
+    # Test for correct behavior of function decorated with
+    # _axis_nan_policy_decorator when function accepts *args
+
+    shape = (3, 8, 9, 10)
+    rng = np.random.default_rng(0)
+    x = rng.random(shape)
+    x[0, 0, 0, 0] = np.nan
+    stats.kruskal(*x)
+
+    message = "kruskal() got an unexpected keyword argument 'samples'"
+    with pytest.raises(TypeError, match=re.escape(message)):
+        stats.kruskal(samples=x)
+
+    with pytest.raises(TypeError, match=re.escape(message)):
+        stats.kruskal(*x, samples=x)
+
+
+def test_axis_nan_policy_decorated_keyword_samples():
+    # Test for correct behavior of function decorated with
+    # _axis_nan_policy_decorator whether samples are provided as positional or
+    # keyword arguments
+
+    shape = (2, 8, 9, 10)
+    rng = np.random.default_rng(0)
+    x = rng.random(shape)
+    x[0, 0, 0, 0] = np.nan
+    res1 = stats.mannwhitneyu(*x)
+    res2 = stats.mannwhitneyu(x=x[0], y=x[1])
+    assert_equal(res1, res2)
+
+    message = "mannwhitneyu() got multiple values for argument"
+    with pytest.raises(TypeError, match=re.escape(message)):
+        stats.mannwhitneyu(*x, x=x[0], y=x[1])
+
+
+@pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "n_outputs",
+                          "paired", "unpacker"), axis_nan_policy_cases)
+def test_axis_nan_policy_decorated_pickled(hypotest, args, kwds, n_samples,
+                                           n_outputs, paired, unpacker):
+    if "ttest_ci" in hypotest.__name__:
+        pytest.skip("Can't pickle functions defined within functions.")
+
+    rng = np.random.default_rng(0)
+
+    # Some hypothesis tests return a non-iterable that needs an `unpacker` to
+    # extract the statistic and p-value. For those that don't:
+    if not unpacker:
+        def unpacker(res):
+            return res
+
+    data = rng.uniform(size=(n_samples, 2, 30))
+    pickled_hypotest = pickle.dumps(hypotest)
+    unpickled_hypotest = pickle.loads(pickled_hypotest)
+    res1 = unpacker(hypotest(*data, *args, axis=-1, **kwds))
+    res2 = unpacker(unpickled_hypotest(*data, *args, axis=-1, **kwds))
+    assert_allclose(res1, res2, rtol=1e-12)
+
+
+def test_check_empty_inputs():
+    # Test that _check_empty_inputs is doing its job, at least for single-
+    # sample inputs. (Multi-sample functionality is tested below.)
+    # If the input sample is not empty, it should return None.
+    # If the input sample is empty, it should return an array of NaNs or an
+    # empty array of appropriate shape. np.mean is used as a reference for the
+    # output because, like the statistics calculated by these functions,
+    # it works along and "consumes" `axis` but preserves the other axes.
+    for i in range(5):
+        for combo in combinations_with_replacement([0, 1, 2], i):
+            for axis in range(len(combo)):
+                samples = (np.zeros(combo),)
+                output = stats._axis_nan_policy._check_empty_inputs(samples,
+                                                                    axis)
+                if output is not None:
+                    with np.testing.suppress_warnings() as sup:
+                        sup.filter(RuntimeWarning, "Mean of empty slice.")
+                        sup.filter(RuntimeWarning, "invalid value encountered")
+                        reference = samples[0].mean(axis=axis)
+                    np.testing.assert_equal(output, reference)
+
+
+def _check_arrays_broadcastable(arrays, axis):
+    # https://numpy.org/doc/stable/user/basics.broadcasting.html
+    # "When operating on two arrays, NumPy compares their shapes element-wise.
+    # It starts with the trailing (i.e. rightmost) dimensions and works its
+    # way left.
+    # Two dimensions are compatible when
+    # 1. they are equal, or
+    # 2. one of them is 1
+    # ...
+    # Arrays do not need to have the same number of dimensions."
+    # (Clarification: if the arrays are compatible according to the criteria
+    #  above and an array runs out of dimensions, it is still compatible.)
+    # Below, we follow the rules above except ignoring `axis`
+
+    n_dims = max([arr.ndim for arr in arrays])
+    if axis is not None:
+        # convert to negative axis
+        axis = (-n_dims + axis) if axis >= 0 else axis
+
+    for dim in range(1, n_dims+1):  # we'll index from -1 to -n_dims, inclusive
+        if -dim == axis:
+            continue  # ignore lengths along `axis`
+
+        dim_lengths = set()
+        for arr in arrays:
+            if dim <= arr.ndim and arr.shape[-dim] != 1:
+                dim_lengths.add(arr.shape[-dim])
+
+        if len(dim_lengths) > 1:
+            return False
+    return True
+
+
+@pytest.mark.slow
+@pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "n_outputs",
+                          "paired", "unpacker"), axis_nan_policy_cases)
+def test_empty(hypotest, args, kwds, n_samples, n_outputs, paired, unpacker):
+    # test for correct output shape when at least one input is empty
+    if hypotest in {stats.kruskal, stats.friedmanchisquare} and not SCIPY_XSLOW:
+        pytest.skip("Too slow.")
+
+    if hypotest in override_propagate_funcs:
+        reason = "Doesn't follow the usual pattern. Tested separately."
+        pytest.skip(reason=reason)
+
+    if unpacker is None:
+        unpacker = lambda res: (res[0], res[1])  # noqa: E731
+
+    def small_data_generator(n_samples, n_dims):
+
+        def small_sample_generator(n_dims):
+            # return all possible "small" arrays in up to n_dim dimensions
+            for i in n_dims:
+                # "small" means with size along dimension either 0 or 1
+                for combo in combinations_with_replacement([0, 1, 2], i):
+                    yield np.zeros(combo)
+
+        # yield all possible combinations of small samples
+        gens = [small_sample_generator(n_dims) for i in range(n_samples)]
+        yield from product(*gens)
+
+    n_dims = [1, 2, 3]
+    for samples in small_data_generator(n_samples, n_dims):
+
+        # this test is only for arrays of zero size
+        if not any(sample.size == 0 for sample in samples):
+            continue
+
+        max_axis = max(sample.ndim for sample in samples)
+
+        # need to test for all valid values of `axis` parameter, too
+        for axis in range(-max_axis, max_axis):
+
+            try:
+                # After broadcasting, all arrays are the same shape, so
+                # the shape of the output should be the same as a single-
+                # sample statistic. Use np.mean as a reference.
+                concat = stats._stats_py._broadcast_concatenate(samples, axis)
+                with np.testing.suppress_warnings() as sup:
+                    sup.filter(RuntimeWarning, "Mean of empty slice.")
+                    sup.filter(RuntimeWarning, "invalid value encountered")
+                    expected = np.mean(concat, axis=axis) * np.nan
+
+                if hypotest in empty_special_case_funcs:
+                    empty_val = hypotest(*([[]]*len(samples)), *args, **kwds)
+                    expected = np.asarray(expected)
+                    mask = np.isnan(expected)
+                    expected[mask] = empty_val
+                    expected = expected[()]
+
+                if expected.size and hypotest not in too_small_special_case_funcs:
+                    message = (too_small_1d_not_omit if max_axis == 1
+                               else too_small_nd_not_omit)
+                    with pytest.warns(SmallSampleWarning, match=message):
+                        res = hypotest(*samples, *args, axis=axis, **kwds)
+                else:
+                    with np.testing.suppress_warnings() as sup:
+                        # f_oneway special case
+                        sup.filter(SmallSampleWarning, "all input arrays have length 1")
+                        res = hypotest(*samples, *args, axis=axis, **kwds)
+                res = unpacker(res)
+
+                for i in range(n_outputs):
+                    assert_equal(res[i], expected)
+
+            except ValueError:
+                # confirm that the arrays truly are not broadcastable
+                assert not _check_arrays_broadcastable(samples,
+                                                       None if paired else axis)
+
+                # confirm that _both_ `_broadcast_concatenate` and `hypotest`
+                # produce this information.
+                message = "Array shapes are incompatible for broadcasting."
+                with pytest.raises(ValueError, match=message):
+                    stats._stats_py._broadcast_concatenate(samples, axis, paired)
+                with pytest.raises(ValueError, match=message):
+                    hypotest(*samples, *args, axis=axis, **kwds)
+
+
+def test_masked_array_2_sentinel_array():
+    # prepare arrays
+    np.random.seed(0)
+    A = np.random.rand(10, 11, 12)
+    B = np.random.rand(12)
+    mask = A < 0.5
+    A = np.ma.masked_array(A, mask)
+
+    # set arbitrary elements to special values
+    # (these values might have been considered for use as sentinel values)
+    max_float = np.finfo(np.float64).max
+    max_float2 = np.nextafter(max_float, -np.inf)
+    max_float3 = np.nextafter(max_float2, -np.inf)
+    A[3, 4, 1] = np.nan
+    A[4, 5, 2] = np.inf
+    A[5, 6, 3] = max_float
+    B[8] = np.nan
+    B[7] = np.inf
+    B[6] = max_float2
+
+    # convert masked A to array with sentinel value, don't modify B
+    out_arrays, sentinel = _masked_arrays_2_sentinel_arrays([A, B])
+    A_out, B_out = out_arrays
+
+    # check that good sentinel value was chosen (according to intended logic)
+    assert (sentinel != max_float) and (sentinel != max_float2)
+    assert sentinel == max_float3
+
+    # check that output arrays are as intended
+    A_reference = A.data
+    A_reference[A.mask] = sentinel
+    np.testing.assert_array_equal(A_out, A_reference)
+    assert B_out is B
+
+
+@skip_xp_invalid_arg
+def test_masked_dtype():
+    # When _masked_arrays_2_sentinel_arrays was first added, it always
+    # upcast the arrays to np.float64. After gh16662, check expected promotion
+    # and that the expected sentinel is found.
+
+    # these are important because the max of the promoted dtype is the first
+    # candidate to be the sentinel value
+    max16 = np.iinfo(np.int16).max
+    max128c = np.finfo(np.complex128).max
+
+    # a is a regular array, b has masked elements, and c has no masked elements
+    a = np.array([1, 2, max16], dtype=np.int16)
+    b = np.ma.array([1, 2, 1], dtype=np.int8, mask=[0, 1, 0])
+    c = np.ma.array([1, 2, 1], dtype=np.complex128, mask=[0, 0, 0])
+
+    # check integer masked -> sentinel conversion
+    out_arrays, sentinel = _masked_arrays_2_sentinel_arrays([a, b])
+    a_out, b_out = out_arrays
+    assert sentinel == max16-1  # not max16 because max16 was in the data
+    assert b_out.dtype == np.int16  # check expected promotion
+    assert_allclose(b_out, [b[0], sentinel, b[-1]])  # check sentinel placement
+    assert a_out is a  # not a masked array, so left untouched
+    assert not isinstance(b_out, np.ma.MaskedArray)  # b became regular array
+
+    # similarly with complex
+    out_arrays, sentinel = _masked_arrays_2_sentinel_arrays([b, c])
+    b_out, c_out = out_arrays
+    assert sentinel == max128c  # max128c was not in the data
+    assert b_out.dtype == np.complex128  # b got promoted
+    assert_allclose(b_out, [b[0], sentinel, b[-1]])  # check sentinel placement
+    assert not isinstance(b_out, np.ma.MaskedArray)  # b became regular array
+    assert not isinstance(c_out, np.ma.MaskedArray)  # c became regular array
+
+    # Also, check edge case when a sentinel value cannot be found in the data
+    min8, max8 = np.iinfo(np.int8).min, np.iinfo(np.int8).max
+    a = np.arange(min8, max8+1, dtype=np.int8)  # use all possible values
+    mask1 = np.zeros_like(a, dtype=bool)
+    mask0 = np.zeros_like(a, dtype=bool)
+
+    # a masked value can be used as the sentinel
+    mask1[1] = True
+    a1 = np.ma.array(a, mask=mask1)
+    out_arrays, sentinel = _masked_arrays_2_sentinel_arrays([a1])
+    assert sentinel == min8+1
+
+    # unless it's the smallest possible; skipped for simiplicity (see code)
+    mask0[0] = True
+    a0 = np.ma.array(a, mask=mask0)
+    message = "This function replaces masked elements with sentinel..."
+    with pytest.raises(ValueError, match=message):
+        _masked_arrays_2_sentinel_arrays([a0])
+
+    # test that dtype is preserved in functions
+    a = np.ma.array([1, 2, 3], mask=[0, 1, 0], dtype=np.float32)
+    assert stats.gmean(a).dtype == np.float32
+
+
+def test_masked_stat_1d():
+    # basic test of _axis_nan_policy_factory with 1D masked sample
+    males = [19, 22, 16, 29, 24]
+    females = [20, 11, 17, 12]
+    res = stats.mannwhitneyu(males, females)
+
+    # same result when extra nan is omitted
+    females2 = [20, 11, 17, np.nan, 12]
+    res2 = stats.mannwhitneyu(males, females2, nan_policy='omit')
+    np.testing.assert_array_equal(res2, res)
+
+    # same result when extra element is masked
+    females3 = [20, 11, 17, 1000, 12]
+    mask3 = [False, False, False, True, False]
+    females3 = np.ma.masked_array(females3, mask=mask3)
+    res3 = stats.mannwhitneyu(males, females3)
+    np.testing.assert_array_equal(res3, res)
+
+    # same result when extra nan is omitted and additional element is masked
+    females4 = [20, 11, 17, np.nan, 1000, 12]
+    mask4 = [False, False, False, False, True, False]
+    females4 = np.ma.masked_array(females4, mask=mask4)
+    res4 = stats.mannwhitneyu(males, females4, nan_policy='omit')
+    np.testing.assert_array_equal(res4, res)
+
+    # same result when extra elements, including nan, are masked
+    females5 = [20, 11, 17, np.nan, 1000, 12]
+    mask5 = [False, False, False, True, True, False]
+    females5 = np.ma.masked_array(females5, mask=mask5)
+    res5 = stats.mannwhitneyu(males, females5, nan_policy='propagate')
+    res6 = stats.mannwhitneyu(males, females5, nan_policy='raise')
+    np.testing.assert_array_equal(res5, res)
+    np.testing.assert_array_equal(res6, res)
+
+
+@pytest.mark.filterwarnings('ignore:After omitting NaNs...')
+@pytest.mark.filterwarnings('ignore:One or more axis-slices of one...')
+@skip_xp_invalid_arg
+@pytest.mark.parametrize(("axis"), range(-3, 3))
+def test_masked_stat_3d(axis):
+    # basic test of _axis_nan_policy_factory with 3D masked sample
+    np.random.seed(0)
+    a = np.random.rand(3, 4, 5)
+    b = np.random.rand(4, 5)
+    c = np.random.rand(4, 1)
+
+    mask_a = a < 0.1
+    mask_c = [False, False, False, True]
+    a_masked = np.ma.masked_array(a, mask=mask_a)
+    c_masked = np.ma.masked_array(c, mask=mask_c)
+
+    a_nans = a.copy()
+    a_nans[mask_a] = np.nan
+    c_nans = c.copy()
+    c_nans[mask_c] = np.nan
+
+    res = stats.kruskal(a_nans, b, c_nans, nan_policy='omit', axis=axis)
+    res2 = stats.kruskal(a_masked, b, c_masked, axis=axis)
+    np.testing.assert_array_equal(res, res2)
+
+
+@pytest.mark.filterwarnings('ignore:After omitting NaNs...')
+@pytest.mark.filterwarnings('ignore:One or more axis-slices of one...')
+@skip_xp_invalid_arg
+def test_mixed_mask_nan_1():
+    # targeted test of _axis_nan_policy_factory with 2D masked sample:
+    # omitting samples with masks and nan_policy='omit' are equivalent
+    # also checks paired-sample sentinel value removal
+    m, n = 3, 20
+    axis = -1
+
+    np.random.seed(0)
+    a = np.random.rand(m, n)
+    b = np.random.rand(m, n)
+    mask_a1 = np.random.rand(m, n) < 0.2
+    mask_a2 = np.random.rand(m, n) < 0.1
+    mask_b1 = np.random.rand(m, n) < 0.15
+    mask_b2 = np.random.rand(m, n) < 0.15
+    mask_a1[2, :] = True
+
+    a_nans = a.copy()
+    b_nans = b.copy()
+    a_nans[mask_a1 | mask_a2] = np.nan
+    b_nans[mask_b1 | mask_b2] = np.nan
+
+    a_masked1 = np.ma.masked_array(a, mask=mask_a1)
+    b_masked1 = np.ma.masked_array(b, mask=mask_b1)
+    a_masked1[mask_a2] = np.nan
+    b_masked1[mask_b2] = np.nan
+
+    a_masked2 = np.ma.masked_array(a, mask=mask_a2)
+    b_masked2 = np.ma.masked_array(b, mask=mask_b2)
+    a_masked2[mask_a1] = np.nan
+    b_masked2[mask_b1] = np.nan
+
+    a_masked3 = np.ma.masked_array(a, mask=(mask_a1 | mask_a2))
+    b_masked3 = np.ma.masked_array(b, mask=(mask_b1 | mask_b2))
+
+    res = stats.wilcoxon(a_nans, b_nans, nan_policy='omit', axis=axis)
+    res1 = stats.wilcoxon(a_masked1, b_masked1, nan_policy='omit', axis=axis)
+    res2 = stats.wilcoxon(a_masked2, b_masked2, nan_policy='omit', axis=axis)
+    res3 = stats.wilcoxon(a_masked3, b_masked3, nan_policy='raise', axis=axis)
+    res4 = stats.wilcoxon(a_masked3, b_masked3,
+                          nan_policy='propagate', axis=axis)
+
+    np.testing.assert_array_equal(res1, res)
+    np.testing.assert_array_equal(res2, res)
+    np.testing.assert_array_equal(res3, res)
+    np.testing.assert_array_equal(res4, res)
+
+
+@pytest.mark.filterwarnings('ignore:After omitting NaNs...')
+@pytest.mark.filterwarnings('ignore:One or more axis-slices of one...')
+@skip_xp_invalid_arg
+def test_mixed_mask_nan_2():
+    # targeted test of _axis_nan_policy_factory with 2D masked sample:
+    # check for expected interaction between masks and nans
+
+    # Cases here are
+    # [mixed nan/mask, all nans, all masked,
+    # unmasked nan, masked nan, unmasked non-nan]
+    a = [[1, np.nan, 2], [np.nan, np.nan, np.nan], [1, 2, 3],
+         [1, np.nan, 3], [1, np.nan, 3], [1, 2, 3]]
+    mask = [[1, 0, 1], [0, 0, 0], [1, 1, 1],
+            [0, 0, 0], [0, 1, 0], [0, 0, 0]]
+    a_masked = np.ma.masked_array(a, mask=mask)
+    b = [[4, 5, 6]]
+    ref1 = stats.ranksums([1, 3], [4, 5, 6])
+    ref2 = stats.ranksums([1, 2, 3], [4, 5, 6])
+
+    # nan_policy = 'omit'
+    # all elements are removed from first three rows
+    # middle element is removed from fourth and fifth rows
+    # no elements removed from last row
+    res = stats.ranksums(a_masked, b, nan_policy='omit', axis=-1)
+    stat_ref = [np.nan, np.nan, np.nan,
+                ref1.statistic, ref1.statistic, ref2.statistic]
+    p_ref = [np.nan, np.nan, np.nan,
+             ref1.pvalue, ref1.pvalue, ref2.pvalue]
+    np.testing.assert_array_equal(res.statistic, stat_ref)
+    np.testing.assert_array_equal(res.pvalue, p_ref)
+
+    # nan_policy = 'propagate'
+    # nans propagate in first, second, and fourth row
+    # all elements are removed by mask from third row
+    # middle element is removed from fifth row
+    # no elements removed from last row
+    res = stats.ranksums(a_masked, b, nan_policy='propagate', axis=-1)
+    stat_ref = [np.nan, np.nan, np.nan,
+                np.nan, ref1.statistic, ref2.statistic]
+    p_ref = [np.nan, np.nan, np.nan,
+             np.nan, ref1.pvalue, ref2.pvalue]
+    np.testing.assert_array_equal(res.statistic, stat_ref)
+    np.testing.assert_array_equal(res.pvalue, p_ref)
+
+
+def test_axis_None_vs_tuple():
+    # `axis` `None` should be equivalent to tuple with all axes
+    shape = (3, 8, 9, 10)
+    rng = np.random.default_rng(0)
+    x = rng.random(shape)
+    res = stats.kruskal(*x, axis=None)
+    res2 = stats.kruskal(*x, axis=(0, 1, 2))
+    np.testing.assert_array_equal(res, res2)
+
+
+def test_axis_None_vs_tuple_with_broadcasting():
+    # `axis` `None` should be equivalent to tuple with all axes,
+    # which should be equivalent to raveling the arrays before passing them
+    rng = np.random.default_rng(0)
+    x = rng.random((5, 1))
+    y = rng.random((1, 5))
+    x2, y2 = np.broadcast_arrays(x, y)
+
+    res0 = stats.mannwhitneyu(x.ravel(), y.ravel())
+    res1 = stats.mannwhitneyu(x, y, axis=None)
+    res2 = stats.mannwhitneyu(x, y, axis=(0, 1))
+    res3 = stats.mannwhitneyu(x2.ravel(), y2.ravel())
+
+    assert res1 == res0
+    assert res2 == res0
+    assert res3 != res0
+
+
+@pytest.mark.parametrize(("axis"),
+                         list(permutations(range(-3, 3), 2)) + [(-4, 1)])
+def test_other_axis_tuples(axis):
+    # Check that _axis_nan_policy_factory treats all `axis` tuples as expected
+    rng = np.random.default_rng(0)
+    shape_x = (4, 5, 6)
+    shape_y = (1, 6)
+    x = rng.random(shape_x)
+    y = rng.random(shape_y)
+    axis_original = axis
+
+    # convert axis elements to positive
+    axis = tuple([(i if i >= 0 else 3 + i) for i in axis])
+    axis = sorted(axis)
+
+    if len(set(axis)) != len(axis):
+        message = "`axis` must contain only distinct elements"
+        with pytest.raises(AxisError, match=re.escape(message)):
+            stats.mannwhitneyu(x, y, axis=axis_original)
+        return
+
+    if axis[0] < 0 or axis[-1] > 2:
+        message = "`axis` is out of bounds for array of dimension 3"
+        with pytest.raises(AxisError, match=re.escape(message)):
+            stats.mannwhitneyu(x, y, axis=axis_original)
+        return
+
+    res = stats.mannwhitneyu(x, y, axis=axis_original)
+
+    # reference behavior
+    not_axis = {0, 1, 2} - set(axis)  # which axis is not part of `axis`
+    not_axis = next(iter(not_axis))  # take it out of the set
+
+    x2 = x
+    shape_y_broadcasted = [1, 1, 6]
+    shape_y_broadcasted[not_axis] = shape_x[not_axis]
+    y2 = np.broadcast_to(y, shape_y_broadcasted)
+
+    m = x2.shape[not_axis]
+    x2 = np.moveaxis(x2, axis, (1, 2))
+    y2 = np.moveaxis(y2, axis, (1, 2))
+    x2 = np.reshape(x2, (m, -1))
+    y2 = np.reshape(y2, (m, -1))
+    res2 = stats.mannwhitneyu(x2, y2, axis=1)
+
+    np.testing.assert_array_equal(res, res2)
+
+
+@pytest.mark.filterwarnings('ignore:After omitting NaNs...')
+@pytest.mark.filterwarnings('ignore:One or more axis-slices of one...')
+@skip_xp_invalid_arg
+@pytest.mark.parametrize(
+    ("weighted_fun_name, unpacker"),
+    [
+        ("gmean", lambda x: x),
+        ("hmean", lambda x: x),
+        ("pmean", lambda x: x),
+        ("combine_pvalues", lambda x: (x.pvalue, x.statistic)),
+    ],
+)
+def test_mean_mixed_mask_nan_weights(weighted_fun_name, unpacker):
+    # targeted test of _axis_nan_policy_factory with 2D masked sample:
+    # omitting samples with masks and nan_policy='omit' are equivalent
+    # also checks paired-sample sentinel value removal
+
+    if weighted_fun_name == 'pmean':
+        def weighted_fun(a, **kwargs):
+            return stats.pmean(a, p=0.42, **kwargs)
+    else:
+        weighted_fun = getattr(stats, weighted_fun_name)
+
+    def func(*args, **kwargs):
+        return unpacker(weighted_fun(*args, **kwargs))
+
+    m, n = 3, 20
+    axis = -1
+
+    rng = np.random.default_rng(6541968121)
+    a = rng.uniform(size=(m, n))
+    b = rng.uniform(size=(m, n))
+    mask_a1 = rng.uniform(size=(m, n)) < 0.2
+    mask_a2 = rng.uniform(size=(m, n)) < 0.1
+    mask_b1 = rng.uniform(size=(m, n)) < 0.15
+    mask_b2 = rng.uniform(size=(m, n)) < 0.15
+    mask_a1[2, :] = True
+
+    a_nans = a.copy()
+    b_nans = b.copy()
+    a_nans[mask_a1 | mask_a2] = np.nan
+    b_nans[mask_b1 | mask_b2] = np.nan
+
+    a_masked1 = np.ma.masked_array(a, mask=mask_a1)
+    b_masked1 = np.ma.masked_array(b, mask=mask_b1)
+    a_masked1[mask_a2] = np.nan
+    b_masked1[mask_b2] = np.nan
+
+    a_masked2 = np.ma.masked_array(a, mask=mask_a2)
+    b_masked2 = np.ma.masked_array(b, mask=mask_b2)
+    a_masked2[mask_a1] = np.nan
+    b_masked2[mask_b1] = np.nan
+
+    a_masked3 = np.ma.masked_array(a, mask=(mask_a1 | mask_a2))
+    b_masked3 = np.ma.masked_array(b, mask=(mask_b1 | mask_b2))
+
+    mask_all = (mask_a1 | mask_a2 | mask_b1 | mask_b2)
+    a_masked4 = np.ma.masked_array(a, mask=mask_all)
+    b_masked4 = np.ma.masked_array(b, mask=mask_all)
+
+    with np.testing.suppress_warnings() as sup:
+        message = 'invalid value encountered'
+        sup.filter(RuntimeWarning, message)
+        res = func(a_nans, weights=b_nans, nan_policy="omit", axis=axis)
+        res1 = func(a_masked1, weights=b_masked1, nan_policy="omit", axis=axis)
+        res2 = func(a_masked2, weights=b_masked2, nan_policy="omit", axis=axis)
+        res3 = func(a_masked3, weights=b_masked3, nan_policy="raise", axis=axis)
+        res4 = func(a_masked3, weights=b_masked3, nan_policy="propagate", axis=axis)
+        # Would test with a_masked3/b_masked3, but there is a bug in np.average
+        # that causes a bug in _no_deco mean with masked weights. Would use
+        # np.ma.average, but that causes other problems. See numpy/numpy#7330.
+        if weighted_fun_name in {"hmean"}:
+            weighted_fun_ma = getattr(stats.mstats, weighted_fun_name)
+            res5 = weighted_fun_ma(a_masked4, weights=b_masked4,
+                                   axis=axis, _no_deco=True)
+
+    np.testing.assert_array_equal(res1, res)
+    np.testing.assert_array_equal(res2, res)
+    np.testing.assert_array_equal(res3, res)
+    np.testing.assert_array_equal(res4, res)
+    if weighted_fun_name in {"hmean"}:
+        # _no_deco mean returns masked array, last element was masked
+        np.testing.assert_allclose(res5.compressed(), res[~np.isnan(res)])
+
+
+def test_raise_invalid_args_g17713():
+    # other cases are handled in:
+    # test_axis_nan_policy_decorated_positional_axis - multiple values for arg
+    # test_axis_nan_policy_decorated_positional_args - unexpected kwd arg
+    message = "got an unexpected keyword argument"
+    with pytest.raises(TypeError, match=message):
+        stats.gmean([1, 2, 3], invalid_arg=True)
+
+    message = " got multiple values for argument"
+    with pytest.raises(TypeError, match=message):
+        stats.gmean([1, 2, 3], a=True)
+
+    message = "missing 1 required positional argument"
+    with pytest.raises(TypeError, match=message):
+        stats.gmean()
+
+    message = "takes from 1 to 4 positional arguments but 5 were given"
+    with pytest.raises(TypeError, match=message):
+        stats.gmean([1, 2, 3], 0, float, [1, 1, 1], 10)
+
+
+@pytest.mark.parametrize('dtype', [np.int16, np.float32, np.complex128])
+def test_array_like_input(dtype):
+    # Check that `_axis_nan_policy`-decorated functions work with custom
+    # containers that are coercible to numeric arrays
+
+    class ArrLike:
+        def __init__(self, x, dtype):
+            self._x = x
+            self._dtype = dtype
+
+        def __array__(self, dtype=None, copy=None):
+            return np.asarray(x, dtype=self._dtype)
+
+    x = [1]*2 + [3, 4, 5]
+    res = stats.mode(ArrLike(x, dtype=dtype))
+    assert res.mode == 1
+    assert res.count == 2

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_binned_statistic.py

@@ -0,0 +1,568 @@
+import numpy as np
+from numpy.testing import assert_allclose
+import pytest
+from pytest import raises as assert_raises
+from scipy.stats import (binned_statistic, binned_statistic_2d,
+                         binned_statistic_dd)
+from scipy._lib._util import check_random_state
+
+from .common_tests import check_named_results
+
+
+class TestBinnedStatistic:
+
+    @classmethod
+    def setup_class(cls):
+        rng = check_random_state(9865)
+        cls.x = rng.uniform(size=100)
+        cls.y = rng.uniform(size=100)
+        cls.v = rng.uniform(size=100)
+        cls.X = rng.uniform(size=(100, 3))
+        cls.w = rng.uniform(size=100)
+        cls.u = rng.uniform(size=100) + 1e6
+
+    def test_1d_count(self):
+        x = self.x
+        v = self.v
+
+        count1, edges1, bc = binned_statistic(x, v, 'count', bins=10)
+        count2, edges2 = np.histogram(x, bins=10)
+
+        assert_allclose(count1, count2)
+        assert_allclose(edges1, edges2)
+
+    def test_gh5927(self):
+        # smoke test for gh5927 - binned_statistic was using `is` for string
+        # comparison
+        x = self.x
+        v = self.v
+        statistics = ['mean', 'median', 'count', 'sum']
+        for statistic in statistics:
+            binned_statistic(x, v, statistic, bins=10)
+
+    def test_big_number_std(self):
+        # tests for numerical stability of std calculation
+        # see issue gh-10126 for more
+        x = self.x
+        u = self.u
+        stat1, edges1, bc = binned_statistic(x, u, 'std', bins=10)
+        stat2, edges2, bc = binned_statistic(x, u, np.std, bins=10)
+
+        assert_allclose(stat1, stat2)
+
+    def test_empty_bins_std(self):
+        # tests that std returns gives nan for empty bins
+        x = self.x
+        u = self.u
+        print(binned_statistic(x, u, 'count', bins=1000))
+        stat1, edges1, bc = binned_statistic(x, u, 'std', bins=1000)
+        stat2, edges2, bc = binned_statistic(x, u, np.std, bins=1000)
+
+        assert_allclose(stat1, stat2)
+
+    def test_non_finite_inputs_and_int_bins(self):
+        # if either `values` or `sample` contain np.inf or np.nan throw
+        # see issue gh-9010 for more
+        x = self.x
+        u = self.u
+        orig = u[0]
+        u[0] = np.inf
+        assert_raises(ValueError, binned_statistic, u, x, 'std', bins=10)
+        # need to test for non-python specific ints, e.g. np.int8, np.int64
+        assert_raises(ValueError, binned_statistic, u, x, 'std',
+                      bins=np.int64(10))
+        u[0] = np.nan
+        assert_raises(ValueError, binned_statistic, u, x, 'count', bins=10)
+        # replace original value, u belongs the class
+        u[0] = orig
+
+    def test_1d_result_attributes(self):
+        x = self.x
+        v = self.v
+
+        res = binned_statistic(x, v, 'count', bins=10)
+        attributes = ('statistic', 'bin_edges', 'binnumber')
+        check_named_results(res, attributes)
+
+    def test_1d_sum(self):
+        x = self.x
+        v = self.v
+
+        sum1, edges1, bc = binned_statistic(x, v, 'sum', bins=10)
+        sum2, edges2 = np.histogram(x, bins=10, weights=v)
+
+        assert_allclose(sum1, sum2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_mean(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'mean', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.mean, bins=10)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_std(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'std', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.std, bins=10)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_min(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'min', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.min, bins=10)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_max(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'max', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.max, bins=10)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_median(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'median', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.median, bins=10)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_bincode(self):
+        x = self.x[:20]
+        v = self.v[:20]
+
+        count1, edges1, bc = binned_statistic(x, v, 'count', bins=3)
+        bc2 = np.array([3, 2, 1, 3, 2, 3, 3, 3, 3, 1, 1, 3, 3, 1, 2, 3, 1,
+                        1, 2, 1])
+
+        bcount = [(bc == i).sum() for i in np.unique(bc)]
+
+        assert_allclose(bc, bc2)
+        assert_allclose(bcount, count1)
+
+    def test_1d_range_keyword(self):
+        # Regression test for gh-3063, range can be (min, max) or [(min, max)]
+        np.random.seed(9865)
+        x = np.arange(30)
+        data = np.random.random(30)
+
+        mean, bins, _ = binned_statistic(x[:15], data[:15])
+        mean_range, bins_range, _ = binned_statistic(x, data, range=[(0, 14)])
+        mean_range2, bins_range2, _ = binned_statistic(x, data, range=(0, 14))
+
+        assert_allclose(mean, mean_range)
+        assert_allclose(bins, bins_range)
+        assert_allclose(mean, mean_range2)
+        assert_allclose(bins, bins_range2)
+
+    def test_1d_multi_values(self):
+        x = self.x
+        v = self.v
+        w = self.w
+
+        stat1v, edges1v, bc1v = binned_statistic(x, v, 'mean', bins=10)
+        stat1w, edges1w, bc1w = binned_statistic(x, w, 'mean', bins=10)
+        stat2, edges2, bc2 = binned_statistic(x, [v, w], 'mean', bins=10)
+
+        assert_allclose(stat2[0], stat1v)
+        assert_allclose(stat2[1], stat1w)
+        assert_allclose(edges1v, edges2)
+        assert_allclose(bc1v, bc2)
+
+    def test_2d_count(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        count1, binx1, biny1, bc = binned_statistic_2d(
+            x, y, v, 'count', bins=5)
+        count2, binx2, biny2 = np.histogram2d(x, y, bins=5)
+
+        assert_allclose(count1, count2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_result_attributes(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        res = binned_statistic_2d(x, y, v, 'count', bins=5)
+        attributes = ('statistic', 'x_edge', 'y_edge', 'binnumber')
+        check_named_results(res, attributes)
+
+    def test_2d_sum(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        sum1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'sum', bins=5)
+        sum2, binx2, biny2 = np.histogram2d(x, y, bins=5, weights=v)
+
+        assert_allclose(sum1, sum2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_mean(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'mean', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.mean, bins=5)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_mean_unicode(self):
+        x = self.x
+        y = self.y
+        v = self.v
+        stat1, binx1, biny1, bc = binned_statistic_2d(
+            x, y, v, 'mean', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.mean, bins=5)
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_std(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'std', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.std, bins=5)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_min(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'min', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.min, bins=5)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_max(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'max', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.max, bins=5)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_median(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(
+            x, y, v, 'median', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(
+            x, y, v, np.median, bins=5)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_bincode(self):
+        x = self.x[:20]
+        y = self.y[:20]
+        v = self.v[:20]
+
+        count1, binx1, biny1, bc = binned_statistic_2d(
+            x, y, v, 'count', bins=3)
+        bc2 = np.array([17, 11, 6, 16, 11, 17, 18, 17, 17, 7, 6, 18, 16,
+                        6, 11, 16, 6, 6, 11, 8])
+
+        bcount = [(bc == i).sum() for i in np.unique(bc)]
+
+        assert_allclose(bc, bc2)
+        count1adj = count1[count1.nonzero()]
+        assert_allclose(bcount, count1adj)
+
+    def test_2d_multi_values(self):
+        x = self.x
+        y = self.y
+        v = self.v
+        w = self.w
+
+        stat1v, binx1v, biny1v, bc1v = binned_statistic_2d(
+            x, y, v, 'mean', bins=8)
+        stat1w, binx1w, biny1w, bc1w = binned_statistic_2d(
+            x, y, w, 'mean', bins=8)
+        stat2, binx2, biny2, bc2 = binned_statistic_2d(
+            x, y, [v, w], 'mean', bins=8)
+
+        assert_allclose(stat2[0], stat1v)
+        assert_allclose(stat2[1], stat1w)
+        assert_allclose(binx1v, binx2)
+        assert_allclose(biny1w, biny2)
+        assert_allclose(bc1v, bc2)
+
+    def test_2d_binnumbers_unraveled(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat, edgesx, bcx = binned_statistic(x, v, 'mean', bins=20)
+        stat, edgesy, bcy = binned_statistic(y, v, 'mean', bins=10)
+
+        stat2, edgesx2, edgesy2, bc2 = binned_statistic_2d(
+            x, y, v, 'mean', bins=(20, 10), expand_binnumbers=True)
+
+        bcx3 = np.searchsorted(edgesx, x, side='right')
+        bcy3 = np.searchsorted(edgesy, y, side='right')
+
+        # `numpy.searchsorted` is non-inclusive on right-edge, compensate
+        bcx3[x == x.max()] -= 1
+        bcy3[y == y.max()] -= 1
+
+        assert_allclose(bcx, bc2[0])
+        assert_allclose(bcy, bc2[1])
+        assert_allclose(bcx3, bc2[0])
+        assert_allclose(bcy3, bc2[1])
+
+    def test_dd_count(self):
+        X = self.X
+        v = self.v
+
+        count1, edges1, bc = binned_statistic_dd(X, v, 'count', bins=3)
+        count2, edges2 = np.histogramdd(X, bins=3)
+
+        assert_allclose(count1, count2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_result_attributes(self):
+        X = self.X
+        v = self.v
+
+        res = binned_statistic_dd(X, v, 'count', bins=3)
+        attributes = ('statistic', 'bin_edges', 'binnumber')
+        check_named_results(res, attributes)
+
+    def test_dd_sum(self):
+        X = self.X
+        v = self.v
+
+        sum1, edges1, bc = binned_statistic_dd(X, v, 'sum', bins=3)
+        sum2, edges2 = np.histogramdd(X, bins=3, weights=v)
+        sum3, edges3, bc = binned_statistic_dd(X, v, np.sum, bins=3)
+
+        assert_allclose(sum1, sum2)
+        assert_allclose(edges1, edges2)
+        assert_allclose(sum1, sum3)
+        assert_allclose(edges1, edges3)
+
+    def test_dd_mean(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'mean', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.mean, bins=3)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_std(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'std', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.std, bins=3)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_min(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'min', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.min, bins=3)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_max(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'max', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.max, bins=3)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_median(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'median', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.median, bins=3)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_bincode(self):
+        X = self.X[:20]
+        v = self.v[:20]
+
+        count1, edges1, bc = binned_statistic_dd(X, v, 'count', bins=3)
+        bc2 = np.array([63, 33, 86, 83, 88, 67, 57, 33, 42, 41, 82, 83, 92,
+                        32, 36, 91, 43, 87, 81, 81])
+
+        bcount = [(bc == i).sum() for i in np.unique(bc)]
+
+        assert_allclose(bc, bc2)
+        count1adj = count1[count1.nonzero()]
+        assert_allclose(bcount, count1adj)
+
+    def test_dd_multi_values(self):
+        X = self.X
+        v = self.v
+        w = self.w
+
+        for stat in ["count", "sum", "mean", "std", "min", "max", "median",
+                     np.std]:
+            stat1v, edges1v, bc1v = binned_statistic_dd(X, v, stat, bins=8)
+            stat1w, edges1w, bc1w = binned_statistic_dd(X, w, stat, bins=8)
+            stat2, edges2, bc2 = binned_statistic_dd(X, [v, w], stat, bins=8)
+            assert_allclose(stat2[0], stat1v)
+            assert_allclose(stat2[1], stat1w)
+            assert_allclose(edges1v, edges2)
+            assert_allclose(edges1w, edges2)
+            assert_allclose(bc1v, bc2)
+
+    def test_dd_binnumbers_unraveled(self):
+        X = self.X
+        v = self.v
+
+        stat, edgesx, bcx = binned_statistic(X[:, 0], v, 'mean', bins=15)
+        stat, edgesy, bcy = binned_statistic(X[:, 1], v, 'mean', bins=20)
+        stat, edgesz, bcz = binned_statistic(X[:, 2], v, 'mean', bins=10)
+
+        stat2, edges2, bc2 = binned_statistic_dd(
+            X, v, 'mean', bins=(15, 20, 10), expand_binnumbers=True)
+
+        assert_allclose(bcx, bc2[0])
+        assert_allclose(bcy, bc2[1])
+        assert_allclose(bcz, bc2[2])
+
+    def test_dd_binned_statistic_result(self):
+        # NOTE: tests the reuse of bin_edges from previous call
+        x = np.random.random((10000, 3))
+        v = np.random.random(10000)
+        bins = np.linspace(0, 1, 10)
+        bins = (bins, bins, bins)
+
+        result = binned_statistic_dd(x, v, 'mean', bins=bins)
+        stat = result.statistic
+
+        result = binned_statistic_dd(x, v, 'mean',
+                                     binned_statistic_result=result)
+        stat2 = result.statistic
+
+        assert_allclose(stat, stat2)
+
+    def test_dd_zero_dedges(self):
+        x = np.random.random((10000, 3))
+        v = np.random.random(10000)
+        bins = np.linspace(0, 1, 10)
+        bins = np.append(bins, 1)
+        bins = (bins, bins, bins)
+        with assert_raises(ValueError, match='difference is numerically 0'):
+            binned_statistic_dd(x, v, 'mean', bins=bins)
+
+    def test_dd_range_errors(self):
+        # Test that descriptive exceptions are raised as appropriate for bad
+        # values of the `range` argument. (See gh-12996)
+        with assert_raises(ValueError,
+                           match='In range, start must be <= stop'):
+            binned_statistic_dd([self.y], self.v,
+                                range=[[1, 0]])
+        with assert_raises(
+                ValueError,
+                match='In dimension 1 of range, start must be <= stop'):
+            binned_statistic_dd([self.x, self.y], self.v,
+                                range=[[1, 0], [0, 1]])
+        with assert_raises(
+                ValueError,
+                match='In dimension 2 of range, start must be <= stop'):
+            binned_statistic_dd([self.x, self.y], self.v,
+                                range=[[0, 1], [1, 0]])
+        with assert_raises(
+                ValueError,
+                match='range given for 1 dimensions; 2 required'):
+            binned_statistic_dd([self.x, self.y], self.v,
+                                range=[[0, 1]])
+
+    def test_binned_statistic_float32(self):
+        X = np.array([0, 0.42358226], dtype=np.float32)
+        stat, _, _ = binned_statistic(X, None, 'count', bins=5)
+        assert_allclose(stat, np.array([1, 0, 0, 0, 1], dtype=np.float64))
+
+    def test_gh14332(self):
+        # Test the wrong output when the `sample` is close to bin edge
+        x = []
+        size = 20
+        for i in range(size):
+            x += [1-0.1**i]
+
+        bins = np.linspace(0,1,11)
+        sum1, edges1, bc = binned_statistic_dd(x, np.ones(len(x)),
+                                               bins=[bins], statistic='sum')
+        sum2, edges2 = np.histogram(x, bins=bins)
+
+        assert_allclose(sum1, sum2)
+        assert_allclose(edges1[0], edges2)
+
+    @pytest.mark.parametrize("dtype", [np.float64, np.complex128])
+    @pytest.mark.parametrize("statistic", [np.mean, np.median, np.sum, np.std,
+                                           np.min, np.max, 'count',
+                                           lambda x: (x**2).sum(),
+                                           lambda x: (x**2).sum() * 1j])
+    def test_dd_all(self, dtype, statistic):
+        def ref_statistic(x):
+            return len(x) if statistic == 'count' else statistic(x)
+
+        rng = np.random.default_rng(3704743126639371)
+        n = 10
+        x = rng.random(size=n)
+        i = x >= 0.5
+        v = rng.random(size=n)
+        if dtype is np.complex128:
+            v = v + rng.random(size=n)*1j
+
+        stat, _, _ = binned_statistic_dd(x, v, statistic, bins=2)
+        ref = np.array([ref_statistic(v[~i]), ref_statistic(v[i])])
+        assert_allclose(stat, ref)
+        assert stat.dtype == np.result_type(ref.dtype, np.float64)

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_censored_data.py

@@ -0,0 +1,152 @@
+# Tests for the CensoredData class.
+
+import pytest
+import numpy as np
+from numpy.testing import assert_equal, assert_array_equal
+from scipy.stats import CensoredData
+
+
+class TestCensoredData:
+
+    def test_basic(self):
+        uncensored = [1]
+        left = [0]
+        right = [2, 5]
+        interval = [[2, 3]]
+        data = CensoredData(uncensored, left=left, right=right,
+                            interval=interval)
+        assert_equal(data._uncensored, uncensored)
+        assert_equal(data._left, left)
+        assert_equal(data._right, right)
+        assert_equal(data._interval, interval)
+
+        udata = data._uncensor()
+        assert_equal(udata, np.concatenate((uncensored, left, right,
+                                            np.mean(interval, axis=1))))
+
+    def test_right_censored(self):
+        x = np.array([0, 3, 2.5])
+        is_censored = np.array([0, 1, 0], dtype=bool)
+        data = CensoredData.right_censored(x, is_censored)
+        assert_equal(data._uncensored, x[~is_censored])
+        assert_equal(data._right, x[is_censored])
+        assert_equal(data._left, [])
+        assert_equal(data._interval, np.empty((0, 2)))
+
+    def test_left_censored(self):
+        x = np.array([0, 3, 2.5])
+        is_censored = np.array([0, 1, 0], dtype=bool)
+        data = CensoredData.left_censored(x, is_censored)
+        assert_equal(data._uncensored, x[~is_censored])
+        assert_equal(data._left, x[is_censored])
+        assert_equal(data._right, [])
+        assert_equal(data._interval, np.empty((0, 2)))
+
+    def test_interval_censored_basic(self):
+        a = [0.5, 2.0, 3.0, 5.5]
+        b = [1.0, 2.5, 3.5, 7.0]
+        data = CensoredData.interval_censored(low=a, high=b)
+        assert_array_equal(data._interval, np.array(list(zip(a, b))))
+        assert data._uncensored.shape == (0,)
+        assert data._left.shape == (0,)
+        assert data._right.shape == (0,)
+
+    def test_interval_censored_mixed(self):
+        # This is actually a mix of uncensored, left-censored, right-censored
+        # and interval-censored data.  Check that when the `interval_censored`
+        # class method is used, the data is correctly separated into the
+        # appropriate arrays.
+        a = [0.5, -np.inf, -13.0, 2.0, 1.0, 10.0, -1.0]
+        b = [0.5, 2500.0, np.inf, 3.0, 1.0, 11.0, np.inf]
+        data = CensoredData.interval_censored(low=a, high=b)
+        assert_array_equal(data._interval, [[2.0, 3.0], [10.0, 11.0]])
+        assert_array_equal(data._uncensored, [0.5, 1.0])
+        assert_array_equal(data._left, [2500.0])
+        assert_array_equal(data._right, [-13.0, -1.0])
+
+    def test_interval_to_other_types(self):
+        # The interval parameter can represent uncensored and
+        # left- or right-censored data.  Test the conversion of such
+        # an example to the canonical form in which the different
+        # types have been split into the separate arrays.
+        interval = np.array([[0, 1],        # interval-censored
+                             [2, 2],        # not censored
+                             [3, 3],        # not censored
+                             [9, np.inf],   # right-censored
+                             [8, np.inf],   # right-censored
+                             [-np.inf, 0],  # left-censored
+                             [1, 2]])       # interval-censored
+        data = CensoredData(interval=interval)
+        assert_equal(data._uncensored, [2, 3])
+        assert_equal(data._left, [0])
+        assert_equal(data._right, [9, 8])
+        assert_equal(data._interval, [[0, 1], [1, 2]])
+
+    def test_empty_arrays(self):
+        data = CensoredData(uncensored=[], left=[], right=[], interval=[])
+        assert data._uncensored.shape == (0,)
+        assert data._left.shape == (0,)
+        assert data._right.shape == (0,)
+        assert data._interval.shape == (0, 2)
+        assert len(data) == 0
+
+    def test_invalid_constructor_args(self):
+        with pytest.raises(ValueError, match='must be a one-dimensional'):
+            CensoredData(uncensored=[[1, 2, 3]])
+        with pytest.raises(ValueError, match='must be a one-dimensional'):
+            CensoredData(left=[[1, 2, 3]])
+        with pytest.raises(ValueError, match='must be a one-dimensional'):
+            CensoredData(right=[[1, 2, 3]])
+        with pytest.raises(ValueError, match='must be a two-dimensional'):
+            CensoredData(interval=[[1, 2, 3]])
+
+        with pytest.raises(ValueError, match='must not contain nan'):
+            CensoredData(uncensored=[1, np.nan, 2])
+        with pytest.raises(ValueError, match='must not contain nan'):
+            CensoredData(left=[1, np.nan, 2])
+        with pytest.raises(ValueError, match='must not contain nan'):
+            CensoredData(right=[1, np.nan, 2])
+        with pytest.raises(ValueError, match='must not contain nan'):
+            CensoredData(interval=[[1, np.nan], [2, 3]])
+
+        with pytest.raises(ValueError,
+                           match='both values must not be infinite'):
+            CensoredData(interval=[[1, 3], [2, 9], [np.inf, np.inf]])
+
+        with pytest.raises(ValueError,
+                           match='left value must not exceed the right'):
+            CensoredData(interval=[[1, 0], [2, 2]])
+
+    @pytest.mark.parametrize('func', [CensoredData.left_censored,
+                                      CensoredData.right_censored])
+    def test_invalid_left_right_censored_args(self, func):
+        with pytest.raises(ValueError,
+                           match='`x` must be one-dimensional'):
+            func([[1, 2, 3]], [0, 1, 1])
+        with pytest.raises(ValueError,
+                           match='`censored` must be one-dimensional'):
+            func([1, 2, 3], [[0, 1, 1]])
+        with pytest.raises(ValueError, match='`x` must not contain'):
+            func([1, 2, np.nan], [0, 1, 1])
+        with pytest.raises(ValueError, match='must have the same length'):
+            func([1, 2, 3], [0, 0, 1, 1])
+
+    def test_invalid_censored_args(self):
+        with pytest.raises(ValueError,
+                           match='`low` must be a one-dimensional'):
+            CensoredData.interval_censored(low=[[3]], high=[4, 5])
+        with pytest.raises(ValueError,
+                           match='`high` must be a one-dimensional'):
+            CensoredData.interval_censored(low=[3], high=[[4, 5]])
+        with pytest.raises(ValueError, match='`low` must not contain'):
+            CensoredData.interval_censored([1, 2, np.nan], [0, 1, 1])
+        with pytest.raises(ValueError, match='must have the same length'):
+            CensoredData.interval_censored([1, 2, 3], [0, 0, 1, 1])
+
+    def test_count_censored(self):
+        x = [1, 2, 3]
+        # data1 has no censored data.
+        data1 = CensoredData(x)
+        assert data1.num_censored() == 0
+        data2 = CensoredData(uncensored=[2.5], left=[10], interval=[[0, 1]])
+        assert data2.num_censored() == 2

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_contingency.py

@@ -0,0 +1,241 @@
+import numpy as np
+from numpy.testing import (assert_equal, assert_array_equal,
+                           assert_array_almost_equal, assert_approx_equal,
+                           assert_allclose)
+import pytest
+from pytest import raises as assert_raises
+from scipy.special import xlogy
+from scipy.stats.contingency import (margins, expected_freq,
+                                     chi2_contingency, association)
+
+
+def test_margins():
+    a = np.array([1])
+    m = margins(a)
+    assert_equal(len(m), 1)
+    m0 = m[0]
+    assert_array_equal(m0, np.array([1]))
+
+    a = np.array([[1]])
+    m0, m1 = margins(a)
+    expected0 = np.array([[1]])
+    expected1 = np.array([[1]])
+    assert_array_equal(m0, expected0)
+    assert_array_equal(m1, expected1)
+
+    a = np.arange(12).reshape(2, 6)
+    m0, m1 = margins(a)
+    expected0 = np.array([[15], [51]])
+    expected1 = np.array([[6, 8, 10, 12, 14, 16]])
+    assert_array_equal(m0, expected0)
+    assert_array_equal(m1, expected1)
+
+    a = np.arange(24).reshape(2, 3, 4)
+    m0, m1, m2 = margins(a)
+    expected0 = np.array([[[66]], [[210]]])
+    expected1 = np.array([[[60], [92], [124]]])
+    expected2 = np.array([[[60, 66, 72, 78]]])
+    assert_array_equal(m0, expected0)
+    assert_array_equal(m1, expected1)
+    assert_array_equal(m2, expected2)
+
+
+def test_expected_freq():
+    assert_array_equal(expected_freq([1]), np.array([1.0]))
+
+    observed = np.array([[[2, 0], [0, 2]], [[0, 2], [2, 0]], [[1, 1], [1, 1]]])
+    e = expected_freq(observed)
+    assert_array_equal(e, np.ones_like(observed))
+
+    observed = np.array([[10, 10, 20], [20, 20, 20]])
+    e = expected_freq(observed)
+    correct = np.array([[12., 12., 16.], [18., 18., 24.]])
+    assert_array_almost_equal(e, correct)
+
+
+def test_chi2_contingency_trivial():
+    # Some very simple tests for chi2_contingency.
+
+    # A trivial case
+    obs = np.array([[1, 2], [1, 2]])
+    chi2, p, dof, expected = chi2_contingency(obs, correction=False)
+    assert_equal(chi2, 0.0)
+    assert_equal(p, 1.0)
+    assert_equal(dof, 1)
+    assert_array_equal(obs, expected)
+
+    # A *really* trivial case: 1-D data.
+    obs = np.array([1, 2, 3])
+    chi2, p, dof, expected = chi2_contingency(obs, correction=False)
+    assert_equal(chi2, 0.0)
+    assert_equal(p, 1.0)
+    assert_equal(dof, 0)
+    assert_array_equal(obs, expected)
+
+
+def test_chi2_contingency_R():
+    # Some test cases that were computed independently, using R.
+
+    # Rcode = \
+    # """
+    # # Data vector.
+    # data <- c(
+    #   12, 34, 23,     4,  47,  11,
+    #   35, 31, 11,    34,  10,  18,
+    #   12, 32,  9,    18,  13,  19,
+    #   12, 12, 14,     9,  33,  25
+    #   )
+    #
+    # # Create factor tags:r=rows, c=columns, t=tiers
+    # r <- factor(gl(4, 2*3, 2*3*4, labels=c("r1", "r2", "r3", "r4")))
+    # c <- factor(gl(3, 1,   2*3*4, labels=c("c1", "c2", "c3")))
+    # t <- factor(gl(2, 3,   2*3*4, labels=c("t1", "t2")))
+    #
+    # # 3-way Chi squared test of independence
+    # s = summary(xtabs(data~r+c+t))
+    # print(s)
+    # """
+    # Routput = \
+    # """
+    # Call: xtabs(formula = data ~ r + c + t)
+    # Number of cases in table: 478
+    # Number of factors: 3
+    # Test for independence of all factors:
+    #         Chisq = 102.17, df = 17, p-value = 3.514e-14
+    # """
+    obs = np.array(
+        [[[12, 34, 23],
+          [35, 31, 11],
+          [12, 32, 9],
+          [12, 12, 14]],
+         [[4, 47, 11],
+          [34, 10, 18],
+          [18, 13, 19],
+          [9, 33, 25]]])
+    chi2, p, dof, expected = chi2_contingency(obs)
+    assert_approx_equal(chi2, 102.17, significant=5)
+    assert_approx_equal(p, 3.514e-14, significant=4)
+    assert_equal(dof, 17)
+
+    # Rcode = \
+    # """
+    # # Data vector.
+    # data <- c(
+    #     #
+    #     12, 17,
+    #     11, 16,
+    #     #
+    #     11, 12,
+    #     15, 16,
+    #     #
+    #     23, 15,
+    #     30, 22,
+    #     #
+    #     14, 17,
+    #     15, 16
+    #     )
+    #
+    # # Create factor tags:r=rows, c=columns, d=depths(?), t=tiers
+    # r <- factor(gl(2, 2,  2*2*2*2, labels=c("r1", "r2")))
+    # c <- factor(gl(2, 1,  2*2*2*2, labels=c("c1", "c2")))
+    # d <- factor(gl(2, 4,  2*2*2*2, labels=c("d1", "d2")))
+    # t <- factor(gl(2, 8,  2*2*2*2, labels=c("t1", "t2")))
+    #
+    # # 4-way Chi squared test of independence
+    # s = summary(xtabs(data~r+c+d+t))
+    # print(s)
+    # """
+    # Routput = \
+    # """
+    # Call: xtabs(formula = data ~ r + c + d + t)
+    # Number of cases in table: 262
+    # Number of factors: 4
+    # Test for independence of all factors:
+    #         Chisq = 8.758, df = 11, p-value = 0.6442
+    # """
+    obs = np.array(
+        [[[[12, 17],
+           [11, 16]],
+          [[11, 12],
+           [15, 16]]],
+         [[[23, 15],
+           [30, 22]],
+          [[14, 17],
+           [15, 16]]]])
+    chi2, p, dof, expected = chi2_contingency(obs)
+    assert_approx_equal(chi2, 8.758, significant=4)
+    assert_approx_equal(p, 0.6442, significant=4)
+    assert_equal(dof, 11)
+
+
+def test_chi2_contingency_g():
+    c = np.array([[15, 60], [15, 90]])
+    g, p, dof, e = chi2_contingency(c, lambda_='log-likelihood',
+                                    correction=False)
+    assert_allclose(g, 2*xlogy(c, c/e).sum())
+
+    g, p, dof, e = chi2_contingency(c, lambda_='log-likelihood',
+                                    correction=True)
+    c_corr = c + np.array([[-0.5, 0.5], [0.5, -0.5]])
+    assert_allclose(g, 2*xlogy(c_corr, c_corr/e).sum())
+
+    c = np.array([[10, 12, 10], [12, 10, 10]])
+    g, p, dof, e = chi2_contingency(c, lambda_='log-likelihood')
+    assert_allclose(g, 2*xlogy(c, c/e).sum())
+
+
+def test_chi2_contingency_bad_args():
+    # Test that "bad" inputs raise a ValueError.
+
+    # Negative value in the array of observed frequencies.
+    obs = np.array([[-1, 10], [1, 2]])
+    assert_raises(ValueError, chi2_contingency, obs)
+
+    # The zeros in this will result in zeros in the array
+    # of expected frequencies.
+    obs = np.array([[0, 1], [0, 1]])
+    assert_raises(ValueError, chi2_contingency, obs)
+
+    # A degenerate case: `observed` has size 0.
+    obs = np.empty((0, 8))
+    assert_raises(ValueError, chi2_contingency, obs)
+
+
+def test_chi2_contingency_yates_gh13875():
+    # Magnitude of Yates' continuity correction should not exceed difference
+    # between expected and observed value of the statistic; see gh-13875
+    observed = np.array([[1573, 3], [4, 0]])
+    p = chi2_contingency(observed)[1]
+    assert_allclose(p, 1, rtol=1e-12)
+
+
+@pytest.mark.parametrize("correction", [False, True])
+def test_result(correction):
+    obs = np.array([[1, 2], [1, 2]])
+    res = chi2_contingency(obs, correction=correction)
+    assert_equal((res.statistic, res.pvalue, res.dof, res.expected_freq), res)
+
+
+def test_bad_association_args():
+    # Invalid Test Statistic
+    assert_raises(ValueError, association, [[1, 2], [3, 4]], "X")
+    # Invalid array shape
+    assert_raises(ValueError, association, [[[1, 2]], [[3, 4]]], "cramer")
+    # chi2_contingency exception
+    assert_raises(ValueError, association, [[-1, 10], [1, 2]], 'cramer')
+    # Invalid Array Item Data Type
+    assert_raises(ValueError, association,
+                  np.array([[1, 2], ["dd", 4]], dtype=object), 'cramer')
+
+
+@pytest.mark.parametrize('stat, expected',
+                         [('cramer', 0.09222412010290792),
+                          ('tschuprow', 0.0775509319944633),
+                          ('pearson', 0.12932925727138758)])
+def test_assoc(stat, expected):
+    # 2d Array
+    obs1 = np.array([[12, 13, 14, 15, 16],
+                     [17, 16, 18, 19, 11],
+                     [9, 15, 14, 12, 11]])
+    a = association(observed=obs1, method=stat)
+    assert_allclose(a, expected)

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_continuous_basic.py

@@ -0,0 +1,1046 @@
+import sys
+import numpy as np
+import numpy.testing as npt
+import pytest
+from pytest import raises as assert_raises
+from scipy.integrate import IntegrationWarning
+import itertools
+
+from scipy import stats
+from .common_tests import (check_normalization, check_moment,
+                           check_mean_expect,
+                           check_var_expect, check_skew_expect,
+                           check_kurt_expect, check_entropy,
+                           check_private_entropy, check_entropy_vect_scale,
+                           check_edge_support, check_named_args,
+                           check_random_state_property,
+                           check_meth_dtype, check_ppf_dtype,
+                           check_cmplx_deriv,
+                           check_pickling, check_rvs_broadcast,
+                           check_freezing, check_munp_expect,)
+from scipy.stats._distr_params import distcont
+from scipy.stats._distn_infrastructure import rv_continuous_frozen
+
+"""
+Test all continuous distributions.
+
+Parameters were chosen for those distributions that pass the
+Kolmogorov-Smirnov test.  This provides safe parameters for each
+distributions so that we can perform further testing of class methods.
+
+These tests currently check only/mostly for serious errors and exceptions,
+not for numerically exact results.
+"""
+
+# Note that you need to add new distributions you want tested
+# to _distr_params
+
+DECIMAL = 5  # specify the precision of the tests  # increased from 0 to 5
+_IS_32BIT = (sys.maxsize < 2**32)
+
+# Sets of tests to skip.
+# Entries sorted by speed (very slow to slow).
+# xslow took > 1s; slow took > 0.5s
+
+xslow_test_cont_basic = {'studentized_range', 'kstwo', 'ksone', 'vonmises', 'kappa4',
+                         'recipinvgauss', 'vonmises_line', 'gausshyper',
+                         'rel_breitwigner', 'norminvgauss'}
+slow_test_cont_basic = {'crystalball', 'powerlognorm', 'pearson3'}
+
+# test_moments is already marked slow
+xslow_test_moments = {'studentized_range', 'ksone', 'vonmises', 'vonmises_line',
+                      'recipinvgauss', 'kstwo', 'kappa4'}
+
+slow_fit_mle = {'exponweib', 'genexpon', 'genhyperbolic', 'johnsonsb',
+                'kappa4', 'powerlognorm', 'tukeylambda'}
+xslow_fit_mle = {'gausshyper', 'ncf', 'ncx2', 'recipinvgauss', 'vonmises_line'}
+xfail_fit_mle = {'ksone', 'kstwo', 'trapezoid', 'truncpareto', 'irwinhall'}
+skip_fit_mle = {'levy_stable', 'studentized_range'}  # far too slow (>10min)
+slow_fit_mm = {'chi2', 'expon', 'lognorm', 'loguniform', 'powerlaw', 'reciprocal'}
+xslow_fit_mm = {'argus', 'beta', 'exponpow', 'gausshyper', 'gengamma',
+                'genhalflogistic', 'geninvgauss', 'gompertz', 'halfgennorm',
+                'johnsonsb', 'kstwobign', 'ncx2', 'norminvgauss', 'truncnorm',
+                'truncweibull_min', 'wrapcauchy'}
+xfail_fit_mm = {'alpha', 'betaprime', 'bradford', 'burr', 'burr12', 'cauchy',
+                'crystalball', 'exponweib', 'f', 'fisk', 'foldcauchy', 'genextreme',
+                'genpareto', 'halfcauchy', 'invgamma', 'irwinhall', 'jf_skew_t',
+                'johnsonsu', 'kappa3', 'kappa4', 'levy', 'levy_l', 'loglaplace',
+                'lomax', 'mielke', 'ncf', 'nct', 'pareto', 'powerlognorm', 'powernorm',
+                'rel_breitwigner',  'skewcauchy', 't', 'trapezoid', 'truncexpon',
+                'truncpareto', 'tukeylambda', 'vonmises', 'vonmises_line'}
+skip_fit_mm = {'genexpon', 'genhyperbolic', 'ksone', 'kstwo', 'levy_stable',
+               'recipinvgauss', 'studentized_range'}  # far too slow (>10min)
+
+# These distributions fail the complex derivative test below.
+# Here 'fail' mean produce wrong results and/or raise exceptions, depending
+# on the implementation details of corresponding special functions.
+# cf https://github.com/scipy/scipy/pull/4979 for a discussion.
+fails_cmplx = {'argus', 'beta', 'betaprime', 'chi', 'chi2', 'cosine',
+               'dgamma', 'dweibull', 'erlang', 'f', 'foldcauchy', 'gamma',
+               'gausshyper', 'gengamma', 'genhyperbolic',
+               'geninvgauss', 'gennorm', 'genpareto',
+               'halfcauchy', 'halfgennorm', 'invgamma', 'irwinhall', 'jf_skew_t',
+               'ksone', 'kstwo', 'kstwobign', 'levy_l', 'loggamma',
+               'logistic', 'loguniform', 'maxwell', 'nakagami',
+               'ncf', 'nct', 'ncx2', 'norminvgauss', 'pearson3',
+               'powerlaw', 'rdist', 'reciprocal', 'rice',
+               'skewnorm', 't', 'truncweibull_min',
+               'tukeylambda', 'vonmises', 'vonmises_line',
+               'rv_histogram_instance', 'truncnorm', 'studentized_range',
+               'johnsonsb', 'halflogistic', 'rel_breitwigner'}
+
+# Slow test_method_with_lists
+slow_with_lists = {'studentized_range'}
+
+
+# rv_histogram instances, with uniform and non-uniform bins;
+# stored as (dist, arg) tuples for cases_test_cont_basic
+# and cases_test_moments.
+histogram_test_instances = []
+case1 = {'a': [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6,
+               6, 6, 6, 7, 7, 7, 8, 8, 9], 'bins': 8}  # equal width bins
+case2 = {'a': [1, 1], 'bins': [0, 1, 10]}  # unequal width bins
+for case, density in itertools.product([case1, case2], [True, False]):
+    _hist = np.histogram(**case, density=density)
+    _rv_hist = stats.rv_histogram(_hist, density=density)
+    histogram_test_instances.append((_rv_hist, tuple()))
+
+
+def cases_test_cont_basic():
+    for distname, arg in distcont[:] + histogram_test_instances:
+        if distname == 'levy_stable':  # fails; tested separately
+            continue
+        if distname in slow_test_cont_basic:
+            yield pytest.param(distname, arg, marks=pytest.mark.slow)
+        elif distname in xslow_test_cont_basic:
+            yield pytest.param(distname, arg, marks=pytest.mark.xslow)
+        else:
+            yield distname, arg
+
+
+@pytest.mark.parametrize('distname,arg', cases_test_cont_basic())
+@pytest.mark.parametrize('sn', [500])
+def test_cont_basic(distname, arg, sn):
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+        distname = 'rv_histogram_instance'
+
+    rng = np.random.RandomState(765456)
+    rvs = distfn.rvs(size=sn, *arg, random_state=rng)
+    m, v = distfn.stats(*arg)
+
+    if distname not in {'laplace_asymmetric'}:
+        check_sample_meanvar_(m, v, rvs)
+    check_cdf_ppf(distfn, arg, distname)
+    check_sf_isf(distfn, arg, distname)
+    check_cdf_sf(distfn, arg, distname)
+    check_ppf_isf(distfn, arg, distname)
+    check_pdf(distfn, arg, distname)
+    check_pdf_logpdf(distfn, arg, distname)
+    check_pdf_logpdf_at_endpoints(distfn, arg, distname)
+    check_cdf_logcdf(distfn, arg, distname)
+    check_sf_logsf(distfn, arg, distname)
+    check_ppf_broadcast(distfn, arg, distname)
+
+    alpha = 0.01
+    if distname == 'rv_histogram_instance':
+        check_distribution_rvs(distfn.cdf, arg, alpha, rvs)
+    elif distname != 'geninvgauss':
+        # skip kstest for geninvgauss since cdf is too slow; see test for
+        # rv generation in TestGenInvGauss in test_distributions.py
+        check_distribution_rvs(distname, arg, alpha, rvs)
+
+    locscale_defaults = (0, 1)
+    meths = [distfn.pdf, distfn.logpdf, distfn.cdf, distfn.logcdf,
+             distfn.logsf]
+    # make sure arguments are within support
+    spec_x = {'weibull_max': -0.5, 'levy_l': -0.5,
+              'pareto': 1.5, 'truncpareto': 3.2, 'tukeylambda': 0.3,
+              'rv_histogram_instance': 5.0}
+    x = spec_x.get(distname, 0.5)
+    if distname == 'invweibull':
+        arg = (1,)
+    elif distname == 'ksone':
+        arg = (3,)
+
+    check_named_args(distfn, x, arg, locscale_defaults, meths)
+    check_random_state_property(distfn, arg)
+
+    if distname in ['rel_breitwigner'] and _IS_32BIT:
+        # gh18414
+        pytest.skip("fails on Linux 32-bit")
+    else:
+        check_pickling(distfn, arg)
+    check_freezing(distfn, arg)
+
+    # Entropy
+    if distname not in ['kstwobign', 'kstwo', 'ncf']:
+        check_entropy(distfn, arg, distname)
+
+    if distfn.numargs == 0:
+        check_vecentropy(distfn, arg)
+
+    if (distfn.__class__._entropy != stats.rv_continuous._entropy
+            and distname != 'vonmises'):
+        check_private_entropy(distfn, arg, stats.rv_continuous)
+
+    with npt.suppress_warnings() as sup:
+        sup.filter(IntegrationWarning, "The occurrence of roundoff error")
+        sup.filter(IntegrationWarning, "Extremely bad integrand")
+        sup.filter(RuntimeWarning, "invalid value")
+        check_entropy_vect_scale(distfn, arg)
+
+    check_retrieving_support(distfn, arg)
+    check_edge_support(distfn, arg)
+
+    check_meth_dtype(distfn, arg, meths)
+    check_ppf_dtype(distfn, arg)
+
+    if distname not in fails_cmplx:
+        check_cmplx_deriv(distfn, arg)
+
+    if distname != 'truncnorm':
+        check_ppf_private(distfn, arg, distname)
+
+
+def cases_test_cont_basic_fit():
+    slow = pytest.mark.slow
+    xslow = pytest.mark.xslow
+    fail = pytest.mark.skip(reason="Test fails and may be slow.")
+    skip = pytest.mark.skip(reason="Test too slow to run to completion (>10m).")
+
+    for distname, arg in distcont[:] + histogram_test_instances:
+        for method in ["MLE", "MM"]:
+            for fix_args in [True, False]:
+                if method == 'MLE' and distname in slow_fit_mle:
+                    yield pytest.param(distname, arg, method, fix_args, marks=slow)
+                    continue
+                if method == 'MLE' and distname in xslow_fit_mle:
+                    yield pytest.param(distname, arg, method, fix_args, marks=xslow)
+                    continue
+                if method == 'MLE' and distname in xfail_fit_mle:
+                    yield pytest.param(distname, arg, method, fix_args, marks=fail)
+                    continue
+                if method == 'MLE' and distname in skip_fit_mle:
+                    yield pytest.param(distname, arg, method, fix_args, marks=skip)
+                    continue
+                if method == 'MM' and distname in slow_fit_mm:
+                    yield pytest.param(distname, arg, method, fix_args, marks=slow)
+                    continue
+                if method == 'MM' and distname in xslow_fit_mm:
+                    yield pytest.param(distname, arg, method, fix_args, marks=xslow)
+                    continue
+                if method == 'MM' and distname in xfail_fit_mm:
+                    yield pytest.param(distname, arg, method, fix_args, marks=fail)
+                    continue
+                if method == 'MM' and distname in skip_fit_mm:
+                    yield pytest.param(distname, arg, method, fix_args, marks=skip)
+                    continue
+
+                yield distname, arg, method, fix_args
+
+
+def test_cont_basic_fit_cases():
+    # Distribution names should not be in multiple MLE or MM sets
+    assert (len(xslow_fit_mle.union(xfail_fit_mle).union(skip_fit_mle)) ==
+            len(xslow_fit_mle) + len(xfail_fit_mle) + len(skip_fit_mle))
+    assert (len(xslow_fit_mm.union(xfail_fit_mm).union(skip_fit_mm)) ==
+            len(xslow_fit_mm) + len(xfail_fit_mm) + len(skip_fit_mm))
+
+
+@pytest.mark.parametrize('distname, arg, method, fix_args',
+                         cases_test_cont_basic_fit())
+@pytest.mark.parametrize('n_fit_samples', [200])
+def test_cont_basic_fit(distname, arg, n_fit_samples, method, fix_args):
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+
+    rng = np.random.RandomState(765456)
+    rvs = distfn.rvs(size=n_fit_samples, *arg, random_state=rng)
+    if fix_args:
+        check_fit_args_fix(distfn, arg, rvs, method)
+    else:
+        check_fit_args(distfn, arg, rvs, method)
+
+@pytest.mark.parametrize('distname,arg', cases_test_cont_basic())
+def test_rvs_scalar(distname, arg):
+    # rvs should return a scalar when given scalar arguments (gh-12428)
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+        distname = 'rv_histogram_instance'
+
+    assert np.isscalar(distfn.rvs(*arg))
+    assert np.isscalar(distfn.rvs(*arg, size=()))
+    assert np.isscalar(distfn.rvs(*arg, size=None))
+
+
+def test_levy_stable_random_state_property():
+    # levy_stable only implements rvs(), so it is skipped in the
+    # main loop in test_cont_basic(). Here we apply just the test
+    # check_random_state_property to levy_stable.
+    check_random_state_property(stats.levy_stable, (0.5, 0.1))
+
+
+def cases_test_moments():
+    fail_normalization = set()
+    fail_higher = {'ncf'}
+    fail_moment = {'johnsonsu'}  # generic `munp` is inaccurate for johnsonsu
+
+    for distname, arg in distcont[:] + histogram_test_instances:
+        if distname == 'levy_stable':
+            continue
+
+        if distname in xslow_test_moments:
+            yield pytest.param(distname, arg, True, True, True, True,
+                               marks=pytest.mark.xslow(reason="too slow"))
+            continue
+
+        cond1 = distname not in fail_normalization
+        cond2 = distname not in fail_higher
+        cond3 = distname not in fail_moment
+
+        marks = list()
+        # Currently unused, `marks` can be used to add a timeout to a test of
+        # a specific distribution.  For example, this shows how a timeout could
+        # be added for the 'skewnorm' distribution:
+        #
+        #     marks = list()
+        #     if distname == 'skewnorm':
+        #         marks.append(pytest.mark.timeout(300))
+
+        yield pytest.param(distname, arg, cond1, cond2, cond3,
+                           False, marks=marks)
+
+        if not cond1 or not cond2 or not cond3:
+            # Run the distributions that have issues twice, once skipping the
+            # not_ok parts, once with the not_ok parts but marked as knownfail
+            yield pytest.param(distname, arg, True, True, True, True,
+                               marks=[pytest.mark.xfail] + marks)
+
+
+@pytest.mark.slow
+@pytest.mark.parametrize('distname,arg,normalization_ok,higher_ok,moment_ok,'
+                         'is_xfailing',
+                         cases_test_moments())
+def test_moments(distname, arg, normalization_ok, higher_ok, moment_ok,
+                 is_xfailing):
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+        distname = 'rv_histogram_instance'
+
+    with npt.suppress_warnings() as sup:
+        sup.filter(IntegrationWarning,
+                   "The integral is probably divergent, or slowly convergent.")
+        sup.filter(IntegrationWarning,
+                   "The maximum number of subdivisions.")
+        sup.filter(IntegrationWarning,
+                   "The algorithm does not converge.")
+
+        if is_xfailing:
+            sup.filter(IntegrationWarning)
+
+        m, v, s, k = distfn.stats(*arg, moments='mvsk')
+
+        with np.errstate(all="ignore"):
+            if normalization_ok:
+                check_normalization(distfn, arg, distname)
+
+            if higher_ok:
+                check_mean_expect(distfn, arg, m, distname)
+                check_skew_expect(distfn, arg, m, v, s, distname)
+                check_var_expect(distfn, arg, m, v, distname)
+                check_kurt_expect(distfn, arg, m, v, k, distname)
+                check_munp_expect(distfn, arg, distname)
+
+        check_loc_scale(distfn, arg, m, v, distname)
+
+        if moment_ok:
+            check_moment(distfn, arg, m, v, distname)
+
+
+@pytest.mark.parametrize('dist,shape_args', distcont)
+def test_rvs_broadcast(dist, shape_args):
+    if dist in ['gausshyper', 'studentized_range']:
+        pytest.skip("too slow")
+
+    if dist in ['rel_breitwigner'] and _IS_32BIT:
+        # gh18414
+        pytest.skip("fails on Linux 32-bit")
+
+    # If shape_only is True, it means the _rvs method of the
+    # distribution uses more than one random number to generate a random
+    # variate.  That means the result of using rvs with broadcasting or
+    # with a nontrivial size will not necessarily be the same as using the
+    # numpy.vectorize'd version of rvs(), so we can only compare the shapes
+    # of the results, not the values.
+    # Whether or not a distribution is in the following list is an
+    # implementation detail of the distribution, not a requirement.  If
+    # the implementation the rvs() method of a distribution changes, this
+    # test might also have to be changed.
+    shape_only = dist in ['argus', 'betaprime', 'dgamma', 'dweibull',
+                          'exponnorm', 'genhyperbolic', 'geninvgauss',
+                          'levy_stable', 'nct', 'norminvgauss', 'rice',
+                          'skewnorm', 'semicircular', 'gennorm', 'loggamma']
+
+    distfunc = getattr(stats, dist)
+    loc = np.zeros(2)
+    scale = np.ones((3, 1))
+    nargs = distfunc.numargs
+    allargs = []
+    bshape = [3, 2]
+    # Generate shape parameter arguments...
+    for k in range(nargs):
+        shp = (k + 4,) + (1,)*(k + 2)
+        allargs.append(shape_args[k]*np.ones(shp))
+        bshape.insert(0, k + 4)
+    allargs.extend([loc, scale])
+    # bshape holds the expected shape when loc, scale, and the shape
+    # parameters are all broadcast together.
+
+    check_rvs_broadcast(distfunc, dist, allargs, bshape, shape_only, 'd')
+
+
+# Expected values of the SF, CDF, PDF were computed using
+# mpmath with mpmath.mp.dps = 50 and output at 20:
+#
+# def ks(x, n):
+#     x = mpmath.mpf(x)
+#     logp = -mpmath.power(6.0*n*x+1.0, 2)/18.0/n
+#     sf, cdf = mpmath.exp(logp), -mpmath.expm1(logp)
+#     pdf = (6.0*n*x+1.0) * 2 * sf/3
+#     print(mpmath.nstr(sf, 20), mpmath.nstr(cdf, 20), mpmath.nstr(pdf, 20))
+#
+# Tests use 1/n < x < 1-1/n and n > 1e6 to use the asymptotic computation.
+# Larger x has a smaller sf.
+@pytest.mark.parametrize('x,n,sf,cdf,pdf,rtol',
+                         [(2.0e-5, 1000000000,
+                           0.44932297307934442379, 0.55067702692065557621,
+                           35946.137394996276407, 5e-15),
+                          (2.0e-9, 1000000000,
+                           0.99999999061111115519, 9.3888888448132728224e-9,
+                           8.6666665852962971765, 5e-14),
+                          (5.0e-4, 1000000000,
+                           7.1222019433090374624e-218, 1.0,
+                           1.4244408634752704094e-211, 5e-14)])
+def test_gh17775_regression(x, n, sf, cdf, pdf, rtol):
+    # Regression test for gh-17775. In scipy 1.9.3 and earlier,
+    # these test would fail.
+    #
+    # KS one asymptotic sf ~ e^(-(6nx+1)^2 / 18n)
+    # Given a large 32-bit integer n, 6n will overflow in the c implementation.
+    # Example of broken behaviour:
+    # ksone.sf(2.0e-5, 1000000000) == 0.9374359693473666
+    ks = stats.ksone
+    vals = np.array([ks.sf(x, n), ks.cdf(x, n), ks.pdf(x, n)])
+    expected = np.array([sf, cdf, pdf])
+    npt.assert_allclose(vals, expected, rtol=rtol)
+    # The sf+cdf must sum to 1.0.
+    npt.assert_equal(vals[0] + vals[1], 1.0)
+    # Check inverting the (potentially very small) sf (uses a lower tolerance)
+    npt.assert_allclose([ks.isf(sf, n)], [x], rtol=1e-8)
+
+
+def test_rvs_gh2069_regression():
+    # Regression tests for gh-2069.  In scipy 0.17 and earlier,
+    # these tests would fail.
+    #
+    # A typical example of the broken behavior:
+    # >>> norm.rvs(loc=np.zeros(5), scale=np.ones(5))
+    # array([-2.49613705, -2.49613705, -2.49613705, -2.49613705, -2.49613705])
+    rng = np.random.RandomState(123)
+    vals = stats.norm.rvs(loc=np.zeros(5), scale=1, random_state=rng)
+    d = np.diff(vals)
+    npt.assert_(np.all(d != 0), "All the values are equal, but they shouldn't be!")
+    vals = stats.norm.rvs(loc=0, scale=np.ones(5), random_state=rng)
+    d = np.diff(vals)
+    npt.assert_(np.all(d != 0), "All the values are equal, but they shouldn't be!")
+    vals = stats.norm.rvs(loc=np.zeros(5), scale=np.ones(5), random_state=rng)
+    d = np.diff(vals)
+    npt.assert_(np.all(d != 0), "All the values are equal, but they shouldn't be!")
+    vals = stats.norm.rvs(loc=np.array([[0], [0]]), scale=np.ones(5),
+                          random_state=rng)
+    d = np.diff(vals.ravel())
+    npt.assert_(np.all(d != 0), "All the values are equal, but they shouldn't be!")
+
+    assert_raises(ValueError, stats.norm.rvs, [[0, 0], [0, 0]],
+                  [[1, 1], [1, 1]], 1)
+    assert_raises(ValueError, stats.gamma.rvs, [2, 3, 4, 5], 0, 1, (2, 2))
+    assert_raises(ValueError, stats.gamma.rvs, [1, 1, 1, 1], [0, 0, 0, 0],
+                  [[1], [2]], (4,))
+
+
+def test_nomodify_gh9900_regression():
+    # Regression test for gh-9990
+    # Prior to gh-9990, calls to stats.truncnorm._cdf() use what ever was
+    # set inside the stats.truncnorm instance during stats.truncnorm.cdf().
+    # This could cause issues with multi-threaded code.
+    # Since then, the calls to cdf() are not permitted to modify the global
+    # stats.truncnorm instance.
+    tn = stats.truncnorm
+    # Use the right-half truncated normal
+    # Check that the cdf and _cdf return the same result.
+    npt.assert_almost_equal(tn.cdf(1, 0, np.inf),
+                            0.6826894921370859)
+    npt.assert_almost_equal(tn._cdf([1], [0], [np.inf]),
+                            0.6826894921370859)
+
+    # Now use the left-half truncated normal
+    npt.assert_almost_equal(tn.cdf(-1, -np.inf, 0),
+                            0.31731050786291415)
+    npt.assert_almost_equal(tn._cdf([-1], [-np.inf], [0]),
+                            0.31731050786291415)
+
+    # Check that the right-half truncated normal _cdf hasn't changed
+    npt.assert_almost_equal(tn._cdf([1], [0], [np.inf]),
+                            0.6826894921370859)  # Not 1.6826894921370859
+    npt.assert_almost_equal(tn.cdf(1, 0, np.inf),
+                            0.6826894921370859)
+
+    # Check that the left-half truncated normal _cdf hasn't changed
+    npt.assert_almost_equal(tn._cdf([-1], [-np.inf], [0]),
+                            0.31731050786291415)  # Not -0.6826894921370859
+    npt.assert_almost_equal(tn.cdf(1, -np.inf, 0),
+                            1)  # Not 1.6826894921370859
+    npt.assert_almost_equal(tn.cdf(-1, -np.inf, 0),
+                            0.31731050786291415)  # Not -0.6826894921370859
+
+
+def test_broadcast_gh9990_regression():
+    # Regression test for gh-9990
+    # The x-value 7 only lies within the support of 4 of the supplied
+    # distributions.  Prior to 9990, one array passed to
+    # stats.reciprocal._cdf would have 4 elements, but an array
+    # previously stored by stats.reciprocal_argcheck() would have 6, leading
+    # to a broadcast error.
+    a = np.array([1, 2, 3, 4, 5, 6])
+    b = np.array([8, 16, 1, 32, 1, 48])
+    ans = [stats.reciprocal.cdf(7, _a, _b) for _a, _b in zip(a,b)]
+    npt.assert_array_almost_equal(stats.reciprocal.cdf(7, a, b), ans)
+
+    ans = [stats.reciprocal.cdf(1, _a, _b) for _a, _b in zip(a,b)]
+    npt.assert_array_almost_equal(stats.reciprocal.cdf(1, a, b), ans)
+
+    ans = [stats.reciprocal.cdf(_a, _a, _b) for _a, _b in zip(a,b)]
+    npt.assert_array_almost_equal(stats.reciprocal.cdf(a, a, b), ans)
+
+    ans = [stats.reciprocal.cdf(_b, _a, _b) for _a, _b in zip(a,b)]
+    npt.assert_array_almost_equal(stats.reciprocal.cdf(b, a, b), ans)
+
+
+def test_broadcast_gh7933_regression():
+    # Check broadcast works
+    stats.truncnorm.logpdf(
+        np.array([3.0, 2.0, 1.0]),
+        a=(1.5 - np.array([6.0, 5.0, 4.0])) / 3.0,
+        b=np.inf,
+        loc=np.array([6.0, 5.0, 4.0]),
+        scale=3.0
+    )
+
+
+def test_gh2002_regression():
+    # Add a check that broadcast works in situations where only some
+    # x-values are compatible with some of the shape arguments.
+    x = np.r_[-2:2:101j]
+    a = np.r_[-np.ones(50), np.ones(51)]
+    expected = [stats.truncnorm.pdf(_x, _a, np.inf) for _x, _a in zip(x, a)]
+    ans = stats.truncnorm.pdf(x, a, np.inf)
+    npt.assert_array_almost_equal(ans, expected)
+
+
+def test_gh1320_regression():
+    # Check that the first example from gh-1320 now works.
+    c = 2.62
+    stats.genextreme.ppf(0.5, np.array([[c], [c + 0.5]]))
+    # The other examples in gh-1320 appear to have stopped working
+    # some time ago.
+    # ans = stats.genextreme.moment(2, np.array([c, c + 0.5]))
+    # expected = np.array([25.50105963, 115.11191437])
+    # stats.genextreme.moment(5, np.array([[c], [c + 0.5]]))
+    # stats.genextreme.moment(5, np.array([c, c + 0.5]))
+
+
+def test_method_of_moments():
+    # example from https://en.wikipedia.org/wiki/Method_of_moments_(statistics)
+    np.random.seed(1234)
+    x = [0, 0, 0, 0, 1]
+    a = 1/5 - 2*np.sqrt(3)/5
+    b = 1/5 + 2*np.sqrt(3)/5
+    # force use of method of moments (uniform.fit is overridden)
+    loc, scale = super(type(stats.uniform), stats.uniform).fit(x, method="MM")
+    npt.assert_almost_equal(loc, a, decimal=4)
+    npt.assert_almost_equal(loc+scale, b, decimal=4)
+
+
+def check_sample_meanvar_(popmean, popvar, sample):
+    if np.isfinite(popmean):
+        check_sample_mean(sample, popmean)
+    if np.isfinite(popvar):
+        check_sample_var(sample, popvar)
+
+
+def check_sample_mean(sample, popmean):
+    # Checks for unlikely difference between sample mean and population mean
+    prob = stats.ttest_1samp(sample, popmean).pvalue
+    assert prob > 0.01
+
+
+def check_sample_var(sample, popvar):
+    # check that population mean lies within the CI bootstrapped from the
+    # sample. This used to be a chi-squared test for variance, but there were
+    # too many false positives
+    res = stats.bootstrap(
+        (sample,),
+        lambda x, axis: x.var(ddof=1, axis=axis),
+        confidence_level=0.995,
+    )
+    conf = res.confidence_interval
+    low, high = conf.low, conf.high
+    assert low <= popvar <= high
+
+
+def check_cdf_ppf(distfn, arg, msg):
+    values = [0.001, 0.5, 0.999]
+    npt.assert_almost_equal(distfn.cdf(distfn.ppf(values, *arg), *arg),
+                            values, decimal=DECIMAL, err_msg=msg +
+                            ' - cdf-ppf roundtrip')
+
+
+def check_sf_isf(distfn, arg, msg):
+    npt.assert_almost_equal(distfn.sf(distfn.isf([0.1, 0.5, 0.9], *arg), *arg),
+                            [0.1, 0.5, 0.9], decimal=DECIMAL, err_msg=msg +
+                            ' - sf-isf roundtrip')
+
+
+def check_cdf_sf(distfn, arg, msg):
+    npt.assert_almost_equal(distfn.cdf([0.1, 0.9], *arg),
+                            1.0 - distfn.sf([0.1, 0.9], *arg),
+                            decimal=DECIMAL, err_msg=msg +
+                            ' - cdf-sf relationship')
+
+
+def check_ppf_isf(distfn, arg, msg):
+    p = np.array([0.1, 0.9])
+    npt.assert_almost_equal(distfn.isf(p, *arg), distfn.ppf(1-p, *arg),
+                            decimal=DECIMAL, err_msg=msg +
+                            ' - ppf-isf relationship')
+
+
+def check_pdf(distfn, arg, msg):
+    # compares pdf at median with numerical derivative of cdf
+    median = distfn.ppf(0.5, *arg)
+    eps = 1e-6
+    pdfv = distfn.pdf(median, *arg)
+    if (pdfv < 1e-4) or (pdfv > 1e4):
+        # avoid checking a case where pdf is close to zero or
+        # huge (singularity)
+        median = median + 0.1
+        pdfv = distfn.pdf(median, *arg)
+    cdfdiff = (distfn.cdf(median + eps, *arg) -
+               distfn.cdf(median - eps, *arg))/eps/2.0
+    # replace with better diff and better test (more points),
+    # actually, this works pretty well
+    msg += ' - cdf-pdf relationship'
+    npt.assert_almost_equal(pdfv, cdfdiff, decimal=DECIMAL, err_msg=msg)
+
+
+def check_pdf_logpdf(distfn, args, msg):
+    # compares pdf at several points with the log of the pdf
+    points = np.array([0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8])
+    vals = distfn.ppf(points, *args)
+    vals = vals[np.isfinite(vals)]
+    pdf = distfn.pdf(vals, *args)
+    logpdf = distfn.logpdf(vals, *args)
+    pdf = pdf[(pdf != 0) & np.isfinite(pdf)]
+    logpdf = logpdf[np.isfinite(logpdf)]
+    msg += " - logpdf-log(pdf) relationship"
+    npt.assert_almost_equal(np.log(pdf), logpdf, decimal=7, err_msg=msg)
+
+
+def check_pdf_logpdf_at_endpoints(distfn, args, msg):
+    # compares pdf with the log of the pdf at the (finite) end points
+    points = np.array([0, 1])
+    vals = distfn.ppf(points, *args)
+    vals = vals[np.isfinite(vals)]
+    pdf = distfn.pdf(vals, *args)
+    logpdf = distfn.logpdf(vals, *args)
+    pdf = pdf[(pdf != 0) & np.isfinite(pdf)]
+    logpdf = logpdf[np.isfinite(logpdf)]
+    msg += " - logpdf-log(pdf) relationship"
+    npt.assert_almost_equal(np.log(pdf), logpdf, decimal=7, err_msg=msg)
+
+
+def check_sf_logsf(distfn, args, msg):
+    # compares sf at several points with the log of the sf
+    points = np.array([0.0, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 1.0])
+    vals = distfn.ppf(points, *args)
+    vals = vals[np.isfinite(vals)]
+    sf = distfn.sf(vals, *args)
+    logsf = distfn.logsf(vals, *args)
+    sf = sf[sf != 0]
+    logsf = logsf[np.isfinite(logsf)]
+    msg += " - logsf-log(sf) relationship"
+    npt.assert_almost_equal(np.log(sf), logsf, decimal=7, err_msg=msg)
+
+
+def check_cdf_logcdf(distfn, args, msg):
+    # compares cdf at several points with the log of the cdf
+    points = np.array([0, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 1.0])
+    vals = distfn.ppf(points, *args)
+    vals = vals[np.isfinite(vals)]
+    cdf = distfn.cdf(vals, *args)
+    logcdf = distfn.logcdf(vals, *args)
+    cdf = cdf[cdf != 0]
+    logcdf = logcdf[np.isfinite(logcdf)]
+    msg += " - logcdf-log(cdf) relationship"
+    npt.assert_almost_equal(np.log(cdf), logcdf, decimal=7, err_msg=msg)
+
+
+def check_ppf_broadcast(distfn, arg, msg):
+    # compares ppf for multiple argsets.
+    num_repeats = 5
+    args = [] * num_repeats
+    if arg:
+        args = [np.array([_] * num_repeats) for _ in arg]
+
+    median = distfn.ppf(0.5, *arg)
+    medians = distfn.ppf(0.5, *args)
+    msg += " - ppf multiple"
+    npt.assert_almost_equal(medians, [median] * num_repeats, decimal=7, err_msg=msg)
+
+
+def check_distribution_rvs(dist, args, alpha, rvs):
+    # dist is either a cdf function or name of a distribution in scipy.stats.
+    # args are the args for scipy.stats.dist(*args)
+    # alpha is a significance level, ~0.01
+    # rvs is array_like of random variables
+    # test from scipy.stats.tests
+    # this version reuses existing random variables
+    D, pval = stats.kstest(rvs, dist, args=args, N=1000)
+    if (pval < alpha):
+        # The rvs passed in failed the K-S test, which _could_ happen
+        # but is unlikely if alpha is small enough.
+        # Repeat the test with a new sample of rvs.
+        # Generate 1000 rvs, perform a K-S test that the new sample of rvs
+        # are distributed according to the distribution.
+        D, pval = stats.kstest(dist, dist, args=args, N=1000)
+        npt.assert_(pval > alpha, "D = " + str(D) + "; pval = " + str(pval) +
+                    "; alpha = " + str(alpha) + "\nargs = " + str(args))
+
+
+def check_vecentropy(distfn, args):
+    npt.assert_equal(distfn.vecentropy(*args), distfn._entropy(*args))
+
+
+def check_loc_scale(distfn, arg, m, v, msg):
+    # Make `loc` and `scale` arrays to catch bugs like gh-13580 where
+    # `loc` and `scale` arrays improperly broadcast with shapes.
+    loc, scale = np.array([10.0, 20.0]), np.array([10.0, 20.0])
+    mt, vt = distfn.stats(*arg, loc=loc, scale=scale)
+    npt.assert_allclose(m*scale + loc, mt)
+    npt.assert_allclose(v*scale*scale, vt)
+
+
+def check_ppf_private(distfn, arg, msg):
+    # fails by design for truncnorm self.nb not defined
+    ppfs = distfn._ppf(np.array([0.1, 0.5, 0.9]), *arg)
+    npt.assert_(not np.any(np.isnan(ppfs)), msg + 'ppf private is nan')
+
+
+def check_retrieving_support(distfn, args):
+    loc, scale = 1, 2
+    supp = distfn.support(*args)
+    supp_loc_scale = distfn.support(*args, loc=loc, scale=scale)
+    npt.assert_almost_equal(np.array(supp)*scale + loc,
+                            np.array(supp_loc_scale))
+
+
+def check_fit_args(distfn, arg, rvs, method):
+    with np.errstate(all='ignore'), npt.suppress_warnings() as sup:
+        sup.filter(category=RuntimeWarning,
+                   message="The shape parameter of the erlang")
+        sup.filter(category=RuntimeWarning,
+                   message="floating point number truncated")
+        vals = distfn.fit(rvs, method=method)
+        vals2 = distfn.fit(rvs, optimizer='powell', method=method)
+    # Only check the length of the return; accuracy tested in test_fit.py
+    npt.assert_(len(vals) == 2+len(arg))
+    npt.assert_(len(vals2) == 2+len(arg))
+
+
+def check_fit_args_fix(distfn, arg, rvs, method):
+    with np.errstate(all='ignore'), npt.suppress_warnings() as sup:
+        sup.filter(category=RuntimeWarning,
+                   message="The shape parameter of the erlang")
+
+        vals = distfn.fit(rvs, floc=0, method=method)
+        vals2 = distfn.fit(rvs, fscale=1, method=method)
+        npt.assert_(len(vals) == 2+len(arg))
+        npt.assert_(vals[-2] == 0)
+        npt.assert_(vals2[-1] == 1)
+        npt.assert_(len(vals2) == 2+len(arg))
+        if len(arg) > 0:
+            vals3 = distfn.fit(rvs, f0=arg[0], method=method)
+            npt.assert_(len(vals3) == 2+len(arg))
+            npt.assert_(vals3[0] == arg[0])
+        if len(arg) > 1:
+            vals4 = distfn.fit(rvs, f1=arg[1], method=method)
+            npt.assert_(len(vals4) == 2+len(arg))
+            npt.assert_(vals4[1] == arg[1])
+        if len(arg) > 2:
+            vals5 = distfn.fit(rvs, f2=arg[2], method=method)
+            npt.assert_(len(vals5) == 2+len(arg))
+            npt.assert_(vals5[2] == arg[2])
+
+
+def cases_test_methods_with_lists():
+    for distname, arg in distcont:
+        if distname in slow_with_lists:
+            yield pytest.param(distname, arg, marks=pytest.mark.slow)
+        else:
+            yield distname, arg
+
+
+@pytest.mark.parametrize('method', ['pdf', 'logpdf', 'cdf', 'logcdf',
+                                    'sf', 'logsf', 'ppf', 'isf'])
+@pytest.mark.parametrize('distname, args', cases_test_methods_with_lists())
+def test_methods_with_lists(method, distname, args):
+    # Test that the continuous distributions can accept Python lists
+    # as arguments.
+    dist = getattr(stats, distname)
+    f = getattr(dist, method)
+    if distname == 'invweibull' and method.startswith('log'):
+        x = [1.5, 2]
+    else:
+        x = [0.1, 0.2]
+
+    shape2 = [[a]*2 for a in args]
+    loc = [0, 0.1]
+    scale = [1, 1.01]
+    result = f(x, *shape2, loc=loc, scale=scale)
+    npt.assert_allclose(result,
+                        [f(*v) for v in zip(x, *shape2, loc, scale)],
+                        rtol=1e-14, atol=5e-14)
+
+
+def test_burr_fisk_moment_gh13234_regression():
+    vals0 = stats.burr.moment(1, 5, 4)
+    assert isinstance(vals0, float)
+
+    vals1 = stats.fisk.moment(1, 8)
+    assert isinstance(vals1, float)
+
+
+def test_moments_with_array_gh12192_regression():
+    # array loc and scalar scale
+    vals0 = stats.norm.moment(order=1, loc=np.array([1, 2, 3]), scale=1)
+    expected0 = np.array([1., 2., 3.])
+    npt.assert_equal(vals0, expected0)
+
+    # array loc and invalid scalar scale
+    vals1 = stats.norm.moment(order=1, loc=np.array([1, 2, 3]), scale=-1)
+    expected1 = np.array([np.nan, np.nan, np.nan])
+    npt.assert_equal(vals1, expected1)
+
+    # array loc and array scale with invalid entries
+    vals2 = stats.norm.moment(order=1, loc=np.array([1, 2, 3]),
+                              scale=[-3, 1, 0])
+    expected2 = np.array([np.nan, 2., np.nan])
+    npt.assert_equal(vals2, expected2)
+
+    # (loc == 0) & (scale < 0)
+    vals3 = stats.norm.moment(order=2, loc=0, scale=-4)
+    expected3 = np.nan
+    npt.assert_equal(vals3, expected3)
+    assert isinstance(vals3, expected3.__class__)
+
+    # array loc with 0 entries and scale with invalid entries
+    vals4 = stats.norm.moment(order=2, loc=[1, 0, 2], scale=[3, -4, -5])
+    expected4 = np.array([10., np.nan, np.nan])
+    npt.assert_equal(vals4, expected4)
+
+    # all(loc == 0) & (array scale with invalid entries)
+    vals5 = stats.norm.moment(order=2, loc=[0, 0, 0], scale=[5., -2, 100.])
+    expected5 = np.array([25., np.nan, 10000.])
+    npt.assert_equal(vals5, expected5)
+
+    # all( (loc == 0) & (scale < 0) )
+    vals6 = stats.norm.moment(order=2, loc=[0, 0, 0], scale=[-5., -2, -100.])
+    expected6 = np.array([np.nan, np.nan, np.nan])
+    npt.assert_equal(vals6, expected6)
+
+    # scalar args, loc, and scale
+    vals7 = stats.chi.moment(order=2, df=1, loc=0, scale=0)
+    expected7 = np.nan
+    npt.assert_equal(vals7, expected7)
+    assert isinstance(vals7, expected7.__class__)
+
+    # array args, scalar loc, and scalar scale
+    vals8 = stats.chi.moment(order=2, df=[1, 2, 3], loc=0, scale=0)
+    expected8 = np.array([np.nan, np.nan, np.nan])
+    npt.assert_equal(vals8, expected8)
+
+    # array args, array loc, and array scale
+    vals9 = stats.chi.moment(order=2, df=[1, 2, 3], loc=[1., 0., 2.],
+                             scale=[1., -3., 0.])
+    expected9 = np.array([3.59576912, np.nan, np.nan])
+    npt.assert_allclose(vals9, expected9, rtol=1e-8)
+
+    # (n > 4), all(loc != 0), and all(scale != 0)
+    vals10 = stats.norm.moment(5, [1., 2.], [1., 2.])
+    expected10 = np.array([26., 832.])
+    npt.assert_allclose(vals10, expected10, rtol=1e-13)
+
+    # test broadcasting and more
+    a = [-1.1, 0, 1, 2.2, np.pi]
+    b = [-1.1, 0, 1, 2.2, np.pi]
+    loc = [-1.1, 0, np.sqrt(2)]
+    scale = [-2.1, 0, 1, 2.2, np.pi]
+
+    a = np.array(a).reshape((-1, 1, 1, 1))
+    b = np.array(b).reshape((-1, 1, 1))
+    loc = np.array(loc).reshape((-1, 1))
+    scale = np.array(scale)
+
+    vals11 = stats.beta.moment(order=2, a=a, b=b, loc=loc, scale=scale)
+
+    a, b, loc, scale = np.broadcast_arrays(a, b, loc, scale)
+
+    for i in np.ndenumerate(a):
+        with np.errstate(invalid='ignore', divide='ignore'):
+            i = i[0]  # just get the index
+            # check against same function with scalar input
+            expected = stats.beta.moment(order=2, a=a[i], b=b[i],
+                                         loc=loc[i], scale=scale[i])
+            np.testing.assert_equal(vals11[i], expected)
+
+
+def test_broadcasting_in_moments_gh12192_regression():
+    vals0 = stats.norm.moment(order=1, loc=np.array([1, 2, 3]), scale=[[1]])
+    expected0 = np.array([[1., 2., 3.]])
+    npt.assert_equal(vals0, expected0)
+    assert vals0.shape == expected0.shape
+
+    vals1 = stats.norm.moment(order=1, loc=np.array([[1], [2], [3]]),
+                              scale=[1, 2, 3])
+    expected1 = np.array([[1., 1., 1.], [2., 2., 2.], [3., 3., 3.]])
+    npt.assert_equal(vals1, expected1)
+    assert vals1.shape == expected1.shape
+
+    vals2 = stats.chi.moment(order=1, df=[1., 2., 3.], loc=0., scale=1.)
+    expected2 = np.array([0.79788456, 1.25331414, 1.59576912])
+    npt.assert_allclose(vals2, expected2, rtol=1e-8)
+    assert vals2.shape == expected2.shape
+
+    vals3 = stats.chi.moment(order=1, df=[[1.], [2.], [3.]], loc=[0., 1., 2.],
+                             scale=[-1., 0., 3.])
+    expected3 = np.array([[np.nan, np.nan, 4.39365368],
+                          [np.nan, np.nan, 5.75994241],
+                          [np.nan, np.nan, 6.78730736]])
+    npt.assert_allclose(vals3, expected3, rtol=1e-8)
+    assert vals3.shape == expected3.shape
+
+
+@pytest.mark.slow
+def test_kappa3_array_gh13582():
+    # https://github.com/scipy/scipy/pull/15140#issuecomment-994958241
+    shapes = [0.5, 1.5, 2.5, 3.5, 4.5]
+    moments = 'mvsk'
+    res = np.array([[stats.kappa3.stats(shape, moments=moment)
+                   for shape in shapes] for moment in moments])
+    res2 = np.array(stats.kappa3.stats(shapes, moments=moments))
+    npt.assert_allclose(res, res2)
+
+
+@pytest.mark.xslow
+def test_kappa4_array_gh13582():
+    h = np.array([-0.5, 2.5, 3.5, 4.5, -3])
+    k = np.array([-0.5, 1, -1.5, 0, 3.5])
+    moments = 'mvsk'
+    res = np.array([[stats.kappa4.stats(h[i], k[i], moments=moment)
+                   for i in range(5)] for moment in moments])
+    res2 = np.array(stats.kappa4.stats(h, k, moments=moments))
+    npt.assert_allclose(res, res2)
+
+    # https://github.com/scipy/scipy/pull/15250#discussion_r775112913
+    h = np.array([-1, -1/4, -1/4, 1, -1, 0])
+    k = np.array([1, 1, 1/2, -1/3, -1, 0])
+    res = np.array([[stats.kappa4.stats(h[i], k[i], moments=moment)
+                   for i in range(6)] for moment in moments])
+    res2 = np.array(stats.kappa4.stats(h, k, moments=moments))
+    npt.assert_allclose(res, res2)
+
+    # https://github.com/scipy/scipy/pull/15250#discussion_r775115021
+    h = np.array([-1, -0.5, 1])
+    k = np.array([-1, -0.5, 0, 1])[:, None]
+    res2 = np.array(stats.kappa4.stats(h, k, moments=moments))
+    assert res2.shape == (4, 4, 3)
+
+
+def test_frozen_attributes():
+    # gh-14827 reported that all frozen distributions had both pmf and pdf
+    # attributes; continuous should have pdf and discrete should have pmf.
+    message = "'rv_continuous_frozen' object has no attribute"
+    with pytest.raises(AttributeError, match=message):
+        stats.norm().pmf
+    with pytest.raises(AttributeError, match=message):
+        stats.norm().logpmf
+    stats.norm.pmf = "herring"
+    frozen_norm = stats.norm()
+    assert isinstance(frozen_norm, rv_continuous_frozen)
+    delattr(stats.norm, 'pmf')
+
+
+def test_skewnorm_pdf_gh16038():
+    rng = np.random.default_rng(0)
+    x, a = -np.inf, 0
+    npt.assert_equal(stats.skewnorm.pdf(x, a), stats.norm.pdf(x))
+    x, a = rng.random(size=(3, 3)), rng.random(size=(3, 3))
+    mask = rng.random(size=(3, 3)) < 0.5
+    a[mask] = 0
+    x_norm = x[mask]
+    res = stats.skewnorm.pdf(x, a)
+    npt.assert_equal(res[mask], stats.norm.pdf(x_norm))
+    npt.assert_equal(res[~mask], stats.skewnorm.pdf(x[~mask], a[~mask]))
+
+
+# for scalar input, these functions should return scalar output
+scalar_out = [['rvs', []], ['pdf', [0]], ['logpdf', [0]], ['cdf', [0]],
+              ['logcdf', [0]], ['sf', [0]], ['logsf', [0]], ['ppf', [0]],
+              ['isf', [0]], ['moment', [1]], ['entropy', []], ['expect', []],
+              ['median', []], ['mean', []], ['std', []], ['var', []]]
+scalars_out = [['interval', [0.95]], ['support', []], ['stats', ['mv']]]
+
+
+@pytest.mark.parametrize('case', scalar_out + scalars_out)
+def test_scalar_for_scalar(case):
+    # Some rv_continuous functions returned 0d array instead of NumPy scalar
+    # Guard against regression
+    method_name, args = case
+    method = getattr(stats.norm(), method_name)
+    res = method(*args)
+    if case in scalar_out:
+        assert isinstance(res, np.number)
+    else:
+        assert isinstance(res[0], np.number)
+        assert isinstance(res[1], np.number)
+
+
+def test_scalar_for_scalar2():
+    # test methods that are not attributes of frozen distributions
+    res = stats.norm.fit([1, 2, 3])
+    assert isinstance(res[0], np.number)
+    assert isinstance(res[1], np.number)
+    res = stats.norm.fit_loc_scale([1, 2, 3])
+    assert isinstance(res[0], np.number)
+    assert isinstance(res[1], np.number)
+    res = stats.norm.nnlf((0, 1), [1, 2, 3])
+    assert isinstance(res, np.number)

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_continuous_fit_censored.py

@@ -0,0 +1,683 @@
+# Tests for fitting specific distributions to censored data.
+
+import numpy as np
+from numpy.testing import assert_allclose
+
+from scipy.optimize import fmin
+from scipy.stats import (CensoredData, beta, cauchy, chi2, expon, gamma,
+                         gumbel_l, gumbel_r, invgauss, invweibull, laplace,
+                         logistic, lognorm, nct, ncx2, norm, weibull_max,
+                         weibull_min)
+
+
+# In some tests, we'll use this optimizer for improved accuracy.
+def optimizer(func, x0, args=(), disp=0):
+    return fmin(func, x0, args=args, disp=disp, xtol=1e-12, ftol=1e-12)
+
+
+def test_beta():
+    """
+    Test fitting beta shape parameters to interval-censored data.
+
+    Calculation in R:
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(0.10, 0.50, 0.75, 0.80),
+    +                    right=c(0.20, 0.55, 0.90, 0.95))
+    > result = fitdistcens(data, 'beta', control=list(reltol=1e-14))
+
+    > result
+    Fitting of the distribution ' beta ' on censored data by maximum likelihood
+    Parameters:
+           estimate
+    shape1 1.419941
+    shape2 1.027066
+    > result$sd
+       shape1    shape2
+    0.9914177 0.6866565
+    """
+    data = CensoredData(interval=[[0.10, 0.20],
+                                  [0.50, 0.55],
+                                  [0.75, 0.90],
+                                  [0.80, 0.95]])
+
+    # For this test, fit only the shape parameters; loc and scale are fixed.
+    a, b, loc, scale = beta.fit(data, floc=0, fscale=1, optimizer=optimizer)
+
+    assert_allclose(a, 1.419941, rtol=5e-6)
+    assert_allclose(b, 1.027066, rtol=5e-6)
+    assert loc == 0
+    assert scale == 1
+
+
+def test_cauchy_right_censored():
+    """
+    Test fitting the Cauchy distribution to right-censored data.
+
+    Calculation in R, with two values not censored [1, 10] and
+    one right-censored value [30].
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(1, 10, 30), right=c(1, 10, NA))
+    > result = fitdistcens(data, 'cauchy', control=list(reltol=1e-14))
+    > result
+    Fitting of the distribution ' cauchy ' on censored data by maximum
+    likelihood
+    Parameters:
+             estimate
+    location 7.100001
+    scale    7.455866
+    """
+    data = CensoredData(uncensored=[1, 10], right=[30])
+    loc, scale = cauchy.fit(data, optimizer=optimizer)
+    assert_allclose(loc, 7.10001, rtol=5e-6)
+    assert_allclose(scale, 7.455866, rtol=5e-6)
+
+
+def test_cauchy_mixed():
+    """
+    Test fitting the Cauchy distribution to data with mixed censoring.
+
+    Calculation in R, with:
+    * two values not censored [1, 10],
+    * one left-censored [1],
+    * one right-censored [30], and
+    * one interval-censored [[4, 8]].
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(NA, 1, 4, 10, 30), right=c(1, 1, 8, 10, NA))
+    > result = fitdistcens(data, 'cauchy', control=list(reltol=1e-14))
+    > result
+    Fitting of the distribution ' cauchy ' on censored data by maximum
+    likelihood
+    Parameters:
+             estimate
+    location 4.605150
+    scale    5.900852
+    """
+    data = CensoredData(uncensored=[1, 10], left=[1], right=[30],
+                        interval=[[4, 8]])
+    loc, scale = cauchy.fit(data, optimizer=optimizer)
+    assert_allclose(loc, 4.605150, rtol=5e-6)
+    assert_allclose(scale, 5.900852, rtol=5e-6)
+
+
+def test_chi2_mixed():
+    """
+    Test fitting just the shape parameter (df) of chi2 to mixed data.
+
+    Calculation in R, with:
+    * two values not censored [1, 10],
+    * one left-censored [1],
+    * one right-censored [30], and
+    * one interval-censored [[4, 8]].
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(NA, 1, 4, 10, 30), right=c(1, 1, 8, 10, NA))
+    > result = fitdistcens(data, 'chisq', control=list(reltol=1e-14))
+    > result
+    Fitting of the distribution ' chisq ' on censored data by maximum
+    likelihood
+    Parameters:
+             estimate
+    df 5.060329
+    """
+    data = CensoredData(uncensored=[1, 10], left=[1], right=[30],
+                        interval=[[4, 8]])
+    df, loc, scale = chi2.fit(data, floc=0, fscale=1, optimizer=optimizer)
+    assert_allclose(df, 5.060329, rtol=5e-6)
+    assert loc == 0
+    assert scale == 1
+
+
+def test_expon_right_censored():
+    """
+    For the exponential distribution with loc=0, the exact solution for
+    fitting n uncensored points x[0]...x[n-1] and m right-censored points
+    x[n]..x[n+m-1] is
+
+        scale = sum(x)/n
+
+    That is, divide the sum of all the values (not censored and
+    right-censored) by the number of uncensored values.  (See, for example,
+    https://en.wikipedia.org/wiki/Censoring_(statistics)#Likelihood.)
+
+    The second derivative of the log-likelihood function is
+
+        n/scale**2 - 2*sum(x)/scale**3
+
+    from which the estimate of the standard error can be computed.
+
+    -----
+
+    Calculation in R, for reference only. The R results are not
+    used in the test.
+
+    > library(fitdistrplus)
+    > dexps <- function(x, scale) {
+    +     return(dexp(x, 1/scale))
+    + }
+    > pexps <- function(q, scale) {
+    +     return(pexp(q, 1/scale))
+    + }
+    > left <- c(1, 2.5, 3, 6, 7.5, 10, 12, 12, 14.5, 15,
+    +                                     16, 16, 20, 20, 21, 22)
+    > right <- c(1, 2.5, 3, 6, 7.5, 10, 12, 12, 14.5, 15,
+    +                                     NA, NA, NA, NA, NA, NA)
+    > result = fitdistcens(data, 'exps', start=list(scale=mean(data$left)),
+    +                      control=list(reltol=1e-14))
+    > result
+    Fitting of the distribution ' exps ' on censored data by maximum likelihood
+    Parameters:
+          estimate
+    scale    19.85
+    > result$sd
+       scale
+    6.277119
+    """
+    # This data has 10 uncensored values and 6 right-censored values.
+    obs = [1, 2.5, 3, 6, 7.5, 10, 12, 12, 14.5, 15, 16, 16, 20, 20, 21, 22]
+    cens = [False]*10 + [True]*6
+    data = CensoredData.right_censored(obs, cens)
+
+    loc, scale = expon.fit(data, floc=0, optimizer=optimizer)
+
+    assert loc == 0
+    # Use the analytical solution to compute the expected value.  This
+    # is the sum of the observed values divided by the number of uncensored
+    # values.
+    n = len(data) - data.num_censored()
+    total = data._uncensored.sum() + data._right.sum()
+    expected = total / n
+    assert_allclose(scale, expected, 1e-8)
+
+
+def test_gamma_right_censored():
+    """
+    Fit gamma shape and scale to data with one right-censored value.
+
+    Calculation in R:
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(2.5, 2.9, 3.8, 9.1, 9.3, 12.0, 23.0, 25.0),
+    +                    right=c(2.5, 2.9, 3.8, 9.1, 9.3, 12.0, 23.0, NA))
+    > result = fitdistcens(data, 'gamma', start=list(shape=1, scale=10),
+    +                      control=list(reltol=1e-13))
+    > result
+    Fitting of the distribution ' gamma ' on censored data by maximum
+      likelihood
+    Parameters:
+          estimate
+    shape 1.447623
+    scale 8.360197
+    > result$sd
+        shape     scale
+    0.7053086 5.1016531
+    """
+    # The last value is right-censored.
+    x = CensoredData.right_censored([2.5, 2.9, 3.8, 9.1, 9.3, 12.0, 23.0,
+                                     25.0],
+                                    [0]*7 + [1])
+
+    a, loc, scale = gamma.fit(x, floc=0, optimizer=optimizer)
+
+    assert_allclose(a, 1.447623, rtol=5e-6)
+    assert loc == 0
+    assert_allclose(scale, 8.360197, rtol=5e-6)
+
+
+def test_gumbel():
+    """
+    Fit gumbel_l and gumbel_r to censored data.
+
+    This R calculation should match gumbel_r.
+
+    > library(evd)
+    > library(fitdistrplus)
+    > data = data.frame(left=c(0, 2, 3, 9, 10, 10),
+    +                   right=c(1, 2, 3, 9, NA, NA))
+    > result = fitdistcens(data, 'gumbel',
+    +                      control=list(reltol=1e-14),
+    +                      start=list(loc=4, scale=5))
+    > result
+    Fitting of the distribution ' gumbel ' on censored data by maximum
+    likelihood
+    Parameters:
+          estimate
+    loc   4.487853
+    scale 4.843640
+    """
+    # First value is interval-censored. Last two are right-censored.
+    uncensored = np.array([2, 3, 9])
+    right = np.array([10, 10])
+    interval = np.array([[0, 1]])
+    data = CensoredData(uncensored, right=right, interval=interval)
+    loc, scale = gumbel_r.fit(data, optimizer=optimizer)
+    assert_allclose(loc, 4.487853, rtol=5e-6)
+    assert_allclose(scale, 4.843640, rtol=5e-6)
+
+    # Negate the data and reverse the intervals, and test with gumbel_l.
+    data2 = CensoredData(-uncensored, left=-right,
+                         interval=-interval[:, ::-1])
+    # Fitting gumbel_l to data2 should give the same result as above, but
+    # with loc negated.
+    loc2, scale2 = gumbel_l.fit(data2, optimizer=optimizer)
+    assert_allclose(loc2, -4.487853, rtol=5e-6)
+    assert_allclose(scale2, 4.843640, rtol=5e-6)
+
+
+def test_invgauss():
+    """
+    Fit just the shape parameter of invgauss to data with one value
+    left-censored and one value right-censored.
+
+    Calculation in R; using a fixed dispersion parameter amounts to fixing
+    the scale to be 1.
+
+    > library(statmod)
+    > library(fitdistrplus)
+    > left <- c(NA, 0.4813096, 0.5571880, 0.5132463, 0.3801414, 0.5904386,
+    +           0.4822340, 0.3478597, 3, 0.7191797, 1.5810902, 0.4442299)
+    > right <- c(0.15, 0.4813096, 0.5571880, 0.5132463, 0.3801414, 0.5904386,
+    +            0.4822340, 0.3478597, NA, 0.7191797, 1.5810902, 0.4442299)
+    > data <- data.frame(left=left, right=right)
+    > result = fitdistcens(data, 'invgauss', control=list(reltol=1e-12),
+    +                      fix.arg=list(dispersion=1), start=list(mean=3))
+    > result
+    Fitting of the distribution ' invgauss ' on censored data by maximum
+      likelihood
+    Parameters:
+         estimate
+    mean 0.853469
+    Fixed parameters:
+               value
+    dispersion     1
+    > result$sd
+        mean
+    0.247636
+
+    Here's the R calculation with the dispersion as a free parameter to
+    be fit.
+
+    > result = fitdistcens(data, 'invgauss', control=list(reltol=1e-12),
+    +                      start=list(mean=3, dispersion=1))
+    > result
+    Fitting of the distribution ' invgauss ' on censored data by maximum
+    likelihood
+    Parameters:
+                estimate
+    mean       0.8699819
+    dispersion 1.2261362
+
+    The parametrization of the inverse Gaussian distribution in the
+    `statmod` package is not the same as in SciPy (see
+        https://arxiv.org/abs/1603.06687
+    for details).  The translation from R to SciPy is
+
+        scale = 1/dispersion
+        mu    = mean * dispersion
+
+    > 1/result$estimate['dispersion']  # 1/dispersion
+    dispersion
+     0.8155701
+    > result$estimate['mean'] * result$estimate['dispersion']
+        mean
+    1.066716
+
+    Those last two values are the SciPy scale and shape parameters.
+    """
+    # One point is left-censored, and one is right-censored.
+    x = [0.4813096, 0.5571880, 0.5132463, 0.3801414,
+         0.5904386, 0.4822340, 0.3478597, 0.7191797,
+         1.5810902, 0.4442299]
+    data = CensoredData(uncensored=x, left=[0.15], right=[3])
+
+    # Fit only the shape parameter.
+    mu, loc, scale = invgauss.fit(data, floc=0, fscale=1, optimizer=optimizer)
+
+    assert_allclose(mu, 0.853469, rtol=5e-5)
+    assert loc == 0
+    assert scale == 1
+
+    # Fit the shape and scale.
+    mu, loc, scale = invgauss.fit(data, floc=0, optimizer=optimizer)
+
+    assert_allclose(mu, 1.066716, rtol=5e-5)
+    assert loc == 0
+    assert_allclose(scale, 0.8155701, rtol=5e-5)
+
+
+def test_invweibull():
+    """
+    Fit invweibull to censored data.
+
+    Here is the calculation in R.  The 'frechet' distribution from the evd
+    package matches SciPy's invweibull distribution.  The `loc` parameter
+    is fixed at 0.
+
+    > library(evd)
+    > library(fitdistrplus)
+    > data = data.frame(left=c(0, 2, 3, 9, 10, 10),
+    +                   right=c(1, 2, 3, 9, NA, NA))
+    > result = fitdistcens(data, 'frechet',
+    +                      control=list(reltol=1e-14),
+    +                      start=list(loc=4, scale=5))
+    > result
+    Fitting of the distribution ' frechet ' on censored data by maximum
+    likelihood
+    Parameters:
+           estimate
+    scale 2.7902200
+    shape 0.6379845
+    Fixed parameters:
+        value
+    loc     0
+    """
+    # In the R data, the first value is interval-censored, and the last
+    # two are right-censored.  The rest are not censored.
+    data = CensoredData(uncensored=[2, 3, 9], right=[10, 10],
+                        interval=[[0, 1]])
+    c, loc, scale = invweibull.fit(data, floc=0, optimizer=optimizer)
+    assert_allclose(c, 0.6379845, rtol=5e-6)
+    assert loc == 0
+    assert_allclose(scale, 2.7902200, rtol=5e-6)
+
+
+def test_laplace():
+    """
+    Fir the Laplace distribution to left- and right-censored data.
+
+    Calculation in R:
+
+    > library(fitdistrplus)
+    > dlaplace <- function(x, location=0, scale=1) {
+    +     return(0.5*exp(-abs((x - location)/scale))/scale)
+    + }
+    > plaplace <- function(q, location=0, scale=1) {
+    +     z <- (q - location)/scale
+    +     s <- sign(z)
+    +     f <- -s*0.5*exp(-abs(z)) + (s+1)/2
+    +     return(f)
+    + }
+    > left <- c(NA, -41.564, 50.0, 15.7384, 50.0, 10.0452, -2.0684,
+    +           -19.5399, 50.0,   9.0005, 27.1227, 4.3113, -3.7372,
+    +           25.3111, 14.7987,  34.0887,  50.0, 42.8496, 18.5862,
+    +           32.8921, 9.0448, -27.4591, NA, 19.5083, -9.7199)
+    > right <- c(-50.0, -41.564,  NA, 15.7384, NA, 10.0452, -2.0684,
+    +            -19.5399, NA, 9.0005, 27.1227, 4.3113, -3.7372,
+    +            25.3111, 14.7987, 34.0887, NA,  42.8496, 18.5862,
+    +            32.8921, 9.0448, -27.4591, -50.0, 19.5083, -9.7199)
+    > data <- data.frame(left=left, right=right)
+    > result <- fitdistcens(data, 'laplace', start=list(location=10, scale=10),
+    +                       control=list(reltol=1e-13))
+    > result
+    Fitting of the distribution ' laplace ' on censored data by maximum
+      likelihood
+    Parameters:
+             estimate
+    location 14.79870
+    scale    30.93601
+    > result$sd
+         location     scale
+    0.1758864 7.0972125
+    """
+    # The value -50 is left-censored, and the value 50 is right-censored.
+    obs = np.array([-50.0, -41.564, 50.0, 15.7384, 50.0, 10.0452, -2.0684,
+                    -19.5399, 50.0, 9.0005, 27.1227, 4.3113, -3.7372,
+                    25.3111, 14.7987, 34.0887, 50.0, 42.8496, 18.5862,
+                    32.8921, 9.0448, -27.4591, -50.0, 19.5083, -9.7199])
+    x = obs[(obs != -50.0) & (obs != 50)]
+    left = obs[obs == -50.0]
+    right = obs[obs == 50.0]
+    data = CensoredData(uncensored=x, left=left, right=right)
+    loc, scale = laplace.fit(data, loc=10, scale=10, optimizer=optimizer)
+    assert_allclose(loc, 14.79870, rtol=5e-6)
+    assert_allclose(scale, 30.93601, rtol=5e-6)
+
+
+def test_logistic():
+    """
+    Fit the logistic distribution to left-censored data.
+
+    Calculation in R:
+    > library(fitdistrplus)
+    > left = c(13.5401, 37.4235, 11.906 , 13.998 ,  NA    ,  0.4023,  NA    ,
+    +          10.9044, 21.0629,  9.6985,  NA    , 12.9016, 39.164 , 34.6396,
+    +          NA    , 20.3665, 16.5889, 18.0952, 45.3818, 35.3306,  8.4949,
+    +          3.4041,  NA    ,  7.2828, 37.1265,  6.5969, 17.6868, 17.4977,
+    +          16.3391, 36.0541)
+    > right = c(13.5401, 37.4235, 11.906 , 13.998 ,  0.    ,  0.4023,  0.    ,
+    +           10.9044, 21.0629,  9.6985,  0.    , 12.9016, 39.164 , 34.6396,
+    +           0.    , 20.3665, 16.5889, 18.0952, 45.3818, 35.3306,  8.4949,
+    +           3.4041,  0.    ,  7.2828, 37.1265,  6.5969, 17.6868, 17.4977,
+    +           16.3391, 36.0541)
+    > data = data.frame(left=left, right=right)
+    > result = fitdistcens(data, 'logis', control=list(reltol=1e-14))
+    > result
+    Fitting of the distribution ' logis ' on censored data by maximum
+      likelihood
+    Parameters:
+              estimate
+    location 14.633459
+    scale     9.232736
+    > result$sd
+    location    scale
+    2.931505 1.546879
+    """
+    # Values that are zero are left-censored; the true values are less than 0.
+    x = np.array([13.5401, 37.4235, 11.906, 13.998, 0.0, 0.4023, 0.0, 10.9044,
+                  21.0629, 9.6985, 0.0, 12.9016, 39.164, 34.6396, 0.0, 20.3665,
+                  16.5889, 18.0952, 45.3818, 35.3306, 8.4949, 3.4041, 0.0,
+                  7.2828, 37.1265, 6.5969, 17.6868, 17.4977, 16.3391,
+                  36.0541])
+    data = CensoredData.left_censored(x, censored=(x == 0))
+    loc, scale = logistic.fit(data, optimizer=optimizer)
+    assert_allclose(loc, 14.633459, rtol=5e-7)
+    assert_allclose(scale, 9.232736, rtol=5e-6)
+
+
+def test_lognorm():
+    """
+    Ref: https://math.montana.edu/jobo/st528/documents/relc.pdf
+
+    The data is the locomotive control time to failure example that starts
+    on page 8.  That's the 8th page in the PDF; the page number shown in
+    the text is 270).
+    The document includes SAS output for the data.
+    """
+    # These are the uncensored measurements.  There are also 59 right-censored
+    # measurements where the lower bound is 135.
+    miles_to_fail = [22.5, 37.5, 46.0, 48.5, 51.5, 53.0, 54.5, 57.5, 66.5,
+                     68.0, 69.5, 76.5, 77.0, 78.5, 80.0, 81.5, 82.0, 83.0,
+                     84.0, 91.5, 93.5, 102.5, 107.0, 108.5, 112.5, 113.5,
+                     116.0, 117.0, 118.5, 119.0, 120.0, 122.5, 123.0, 127.5,
+                     131.0, 132.5, 134.0]
+
+    data = CensoredData.right_censored(miles_to_fail + [135]*59,
+                                       [0]*len(miles_to_fail) + [1]*59)
+    sigma, loc, scale = lognorm.fit(data, floc=0)
+
+    assert loc == 0
+    # Convert the lognorm parameters to the mu and sigma of the underlying
+    # normal distribution.
+    mu = np.log(scale)
+    # The expected results are from the 17th page of the PDF document
+    # (labeled page 279), in the SAS output on the right side of the page.
+    assert_allclose(mu, 5.1169, rtol=5e-4)
+    assert_allclose(sigma, 0.7055, rtol=5e-3)
+
+
+def test_nct():
+    """
+    Test fitting the noncentral t distribution to censored data.
+
+    Calculation in R:
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(1, 2, 3, 5, 8, 10, 25, 25),
+    +                    right=c(1, 2, 3, 5, 8, 10, NA, NA))
+    > result = fitdistcens(data, 't', control=list(reltol=1e-14),
+    +                      start=list(df=1, ncp=2))
+    > result
+    Fitting of the distribution ' t ' on censored data by maximum likelihood
+    Parameters:
+         estimate
+    df  0.5432336
+    ncp 2.8893565
+
+    """
+    data = CensoredData.right_censored([1, 2, 3, 5, 8, 10, 25, 25],
+                                       [0, 0, 0, 0, 0, 0, 1, 1])
+    # Fit just the shape parameter df and nc; loc and scale are fixed.
+    with np.errstate(over='ignore'):  # remove context when gh-14901 is closed
+        df, nc, loc, scale = nct.fit(data, floc=0, fscale=1,
+                                     optimizer=optimizer)
+    assert_allclose(df, 0.5432336, rtol=5e-6)
+    assert_allclose(nc, 2.8893565, rtol=5e-6)
+    assert loc == 0
+    assert scale == 1
+
+
+def test_ncx2():
+    """
+    Test fitting the shape parameters (df, ncp) of ncx2 to mixed data.
+
+    Calculation in R, with
+    * 5 not censored values [2.7, 0.2, 6.5, 0.4, 0.1],
+    * 1 interval-censored value [[0.6, 1.0]], and
+    * 2 right-censored values [8, 8].
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(2.7, 0.2, 6.5, 0.4, 0.1, 0.6, 8, 8),
+    +                    right=c(2.7, 0.2, 6.5, 0.4, 0.1, 1.0, NA, NA))
+    > result = fitdistcens(data, 'chisq', control=list(reltol=1e-14),
+    +                      start=list(df=1, ncp=2))
+    > result
+    Fitting of the distribution ' chisq ' on censored data by maximum
+    likelihood
+    Parameters:
+        estimate
+    df  1.052871
+    ncp 2.362934
+    """
+    data = CensoredData(uncensored=[2.7, 0.2, 6.5, 0.4, 0.1], right=[8, 8],
+                        interval=[[0.6, 1.0]])
+    with np.errstate(over='ignore'):  # remove context when gh-14901 is closed
+        df, ncp, loc, scale = ncx2.fit(data, floc=0, fscale=1,
+                                       optimizer=optimizer)
+    assert_allclose(df, 1.052871, rtol=5e-6)
+    assert_allclose(ncp, 2.362934, rtol=5e-6)
+    assert loc == 0
+    assert scale == 1
+
+
+def test_norm():
+    """
+    Test fitting the normal distribution to interval-censored data.
+
+    Calculation in R:
+
+    > library(fitdistrplus)
+    > data <- data.frame(left=c(0.10, 0.50, 0.75, 0.80),
+    +                    right=c(0.20, 0.55, 0.90, 0.95))
+    > result = fitdistcens(data, 'norm', control=list(reltol=1e-14))
+
+    > result
+    Fitting of the distribution ' norm ' on censored data by maximum likelihood
+    Parameters:
+          estimate
+    mean 0.5919990
+    sd   0.2868042
+    > result$sd
+         mean        sd
+    0.1444432 0.1029451
+    """
+    data = CensoredData(interval=[[0.10, 0.20],
+                                  [0.50, 0.55],
+                                  [0.75, 0.90],
+                                  [0.80, 0.95]])
+
+    loc, scale = norm.fit(data, optimizer=optimizer)
+
+    assert_allclose(loc, 0.5919990, rtol=5e-6)
+    assert_allclose(scale, 0.2868042, rtol=5e-6)
+
+
+def test_weibull_censored1():
+    # Ref: http://www.ams.sunysb.edu/~zhu/ams588/Lecture_3_likelihood.pdf
+
+    # Survival times; '*' indicates right-censored.
+    s = "3,5,6*,8,10*,11*,15,20*,22,23,27*,29,32,35,40,26,28,33*,21,24*"
+
+    times, cens = zip(*[(float(t[0]), len(t) == 2)
+                        for t in [w.split('*') for w in s.split(',')]])
+    data = CensoredData.right_censored(times, cens)
+
+    c, loc, scale = weibull_min.fit(data, floc=0)
+
+    # Expected values are from the reference.
+    assert_allclose(c, 2.149, rtol=1e-3)
+    assert loc == 0
+    assert_allclose(scale, 28.99, rtol=1e-3)
+
+    # Flip the sign of the data, and make the censored values
+    # left-censored. We should get the same parameters when we fit
+    # weibull_max to the flipped data.
+    data2 = CensoredData.left_censored(-np.array(times), cens)
+
+    c2, loc2, scale2 = weibull_max.fit(data2, floc=0)
+
+    assert_allclose(c2, 2.149, rtol=1e-3)
+    assert loc2 == 0
+    assert_allclose(scale2, 28.99, rtol=1e-3)
+
+
+def test_weibull_min_sas1():
+    # Data and SAS results from
+    #   https://support.sas.com/documentation/cdl/en/qcug/63922/HTML/default/
+    #         viewer.htm#qcug_reliability_sect004.htm
+
+    text = """
+           450 0    460 1   1150 0   1150 0   1560 1
+          1600 0   1660 1   1850 1   1850 1   1850 1
+          1850 1   1850 1   2030 1   2030 1   2030 1
+          2070 0   2070 0   2080 0   2200 1   3000 1
+          3000 1   3000 1   3000 1   3100 0   3200 1
+          3450 0   3750 1   3750 1   4150 1   4150 1
+          4150 1   4150 1   4300 1   4300 1   4300 1
+          4300 1   4600 0   4850 1   4850 1   4850 1
+          4850 1   5000 1   5000 1   5000 1   6100 1
+          6100 0   6100 1   6100 1   6300 1   6450 1
+          6450 1   6700 1   7450 1   7800 1   7800 1
+          8100 1   8100 1   8200 1   8500 1   8500 1
+          8500 1   8750 1   8750 0   8750 1   9400 1
+          9900 1  10100 1  10100 1  10100 1  11500 1
+    """
+
+    life, cens = np.array([int(w) for w in text.split()]).reshape(-1, 2).T
+    life = life/1000.0
+
+    data = CensoredData.right_censored(life, cens)
+
+    c, loc, scale = weibull_min.fit(data, floc=0, optimizer=optimizer)
+    assert_allclose(c, 1.0584, rtol=1e-4)
+    assert_allclose(scale, 26.2968, rtol=1e-5)
+    assert loc == 0
+
+
+def test_weibull_min_sas2():
+    # http://support.sas.com/documentation/cdl/en/ormpug/67517/HTML/default/
+    #      viewer.htm#ormpug_nlpsolver_examples06.htm
+
+    # The last two values are right-censored.
+    days = np.array([143, 164, 188, 188, 190, 192, 206, 209, 213, 216, 220,
+                     227, 230, 234, 246, 265, 304, 216, 244])
+
+    data = CensoredData.right_censored(days, [0]*(len(days) - 2) + [1]*2)
+
+    c, loc, scale = weibull_min.fit(data, 1, loc=100, scale=100,
+                                    optimizer=optimizer)
+
+    assert_allclose(c, 2.7112, rtol=5e-4)
+    assert_allclose(loc, 122.03, rtol=5e-4)
+    assert_allclose(scale, 108.37, rtol=5e-4)

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_crosstab.py

@@ -0,0 +1,115 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_array_equal, assert_equal
+from scipy.stats.contingency import crosstab
+
+
+@pytest.mark.parametrize('sparse', [False, True])
+def test_crosstab_basic(sparse):
+    a = [0, 0, 9, 9, 0, 0, 9]
+    b = [2, 1, 3, 1, 2, 3, 3]
+    expected_avals = [0, 9]
+    expected_bvals = [1, 2, 3]
+    expected_count = np.array([[1, 2, 1],
+                               [1, 0, 2]])
+    (avals, bvals), count = crosstab(a, b, sparse=sparse)
+    assert_array_equal(avals, expected_avals)
+    assert_array_equal(bvals, expected_bvals)
+    if sparse:
+        assert_array_equal(count.toarray(), expected_count)
+    else:
+        assert_array_equal(count, expected_count)
+
+
+def test_crosstab_basic_1d():
+    # Verify that a single input sequence works as expected.
+    x = [1, 2, 3, 1, 2, 3, 3]
+    expected_xvals = [1, 2, 3]
+    expected_count = np.array([2, 2, 3])
+    (xvals,), count = crosstab(x)
+    assert_array_equal(xvals, expected_xvals)
+    assert_array_equal(count, expected_count)
+
+
+def test_crosstab_basic_3d():
+    # Verify the function for three input sequences.
+    a = 'a'
+    b = 'b'
+    x = [0, 0, 9, 9, 0, 0, 9, 9]
+    y = [a, a, a, a, b, b, b, a]
+    z = [1, 2, 3, 1, 2, 3, 3, 1]
+    expected_xvals = [0, 9]
+    expected_yvals = [a, b]
+    expected_zvals = [1, 2, 3]
+    expected_count = np.array([[[1, 1, 0],
+                                [0, 1, 1]],
+                               [[2, 0, 1],
+                                [0, 0, 1]]])
+    (xvals, yvals, zvals), count = crosstab(x, y, z)
+    assert_array_equal(xvals, expected_xvals)
+    assert_array_equal(yvals, expected_yvals)
+    assert_array_equal(zvals, expected_zvals)
+    assert_array_equal(count, expected_count)
+
+
+@pytest.mark.parametrize('sparse', [False, True])
+def test_crosstab_levels(sparse):
+    a = [0, 0, 9, 9, 0, 0, 9]
+    b = [1, 2, 3, 1, 2, 3, 3]
+    expected_avals = [0, 9]
+    expected_bvals = [0, 1, 2, 3]
+    expected_count = np.array([[0, 1, 2, 1],
+                               [0, 1, 0, 2]])
+    (avals, bvals), count = crosstab(a, b, levels=[None, [0, 1, 2, 3]],
+                                     sparse=sparse)
+    assert_array_equal(avals, expected_avals)
+    assert_array_equal(bvals, expected_bvals)
+    if sparse:
+        assert_array_equal(count.toarray(), expected_count)
+    else:
+        assert_array_equal(count, expected_count)
+
+
+@pytest.mark.parametrize('sparse', [False, True])
+def test_crosstab_extra_levels(sparse):
+    # The pair of values (-1, 3) will be ignored, because we explicitly
+    # request the counted `a` values to be [0, 9].
+    a = [0, 0, 9, 9, 0, 0, 9, -1]
+    b = [1, 2, 3, 1, 2, 3, 3, 3]
+    expected_avals = [0, 9]
+    expected_bvals = [0, 1, 2, 3]
+    expected_count = np.array([[0, 1, 2, 1],
+                               [0, 1, 0, 2]])
+    (avals, bvals), count = crosstab(a, b, levels=[[0, 9], [0, 1, 2, 3]],
+                                     sparse=sparse)
+    assert_array_equal(avals, expected_avals)
+    assert_array_equal(bvals, expected_bvals)
+    if sparse:
+        assert_array_equal(count.toarray(), expected_count)
+    else:
+        assert_array_equal(count, expected_count)
+
+
+def test_validation_at_least_one():
+    with pytest.raises(TypeError, match='At least one'):
+        crosstab()
+
+
+def test_validation_same_lengths():
+    with pytest.raises(ValueError, match='must have the same length'):
+        crosstab([1, 2], [1, 2, 3, 4])
+
+
+def test_validation_sparse_only_two_args():
+    with pytest.raises(ValueError, match='only two input sequences'):
+        crosstab([0, 1, 1], [8, 8, 9], [1, 3, 3], sparse=True)
+
+
+def test_validation_len_levels_matches_args():
+    with pytest.raises(ValueError, match='number of input sequences'):
+        crosstab([0, 1, 1], [8, 8, 9], levels=([0, 1, 2, 3],))
+
+
+def test_result():
+    res = crosstab([0, 1], [1, 2])
+    assert_equal((res.elements, res.count), res)

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_discrete_basic.py

@@ -0,0 +1,563 @@
+import numpy.testing as npt
+from numpy.testing import assert_allclose
+
+import numpy as np
+import pytest
+
+from scipy import stats
+from .common_tests import (check_normalization, check_moment,
+                           check_mean_expect,
+                           check_var_expect, check_skew_expect,
+                           check_kurt_expect, check_entropy,
+                           check_private_entropy, check_edge_support,
+                           check_named_args, check_random_state_property,
+                           check_pickling, check_rvs_broadcast,
+                           check_freezing,)
+from scipy.stats._distr_params import distdiscrete, invdistdiscrete
+from scipy.stats._distn_infrastructure import rv_discrete_frozen
+
+vals = ([1, 2, 3, 4], [0.1, 0.2, 0.3, 0.4])
+distdiscrete += [[stats.rv_discrete(values=vals), ()]]
+
+# For these distributions, test_discrete_basic only runs with test mode full
+distslow = {'zipfian', 'nhypergeom'}
+
+# Override number of ULPs adjustment for `check_cdf_ppf`
+roundtrip_cdf_ppf_exceptions = {'nbinom': 30}
+
+def cases_test_discrete_basic():
+    seen = set()
+    for distname, arg in distdiscrete:
+        if distname in distslow:
+            yield pytest.param(distname, arg, distname, marks=pytest.mark.slow)
+        else:
+            yield distname, arg, distname not in seen
+        seen.add(distname)
+
+
+@pytest.mark.parametrize('distname,arg,first_case', cases_test_discrete_basic())
+def test_discrete_basic(distname, arg, first_case):
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+        distname = 'sample distribution'
+    np.random.seed(9765456)
+    rvs = distfn.rvs(size=2000, *arg)
+    supp = np.unique(rvs)
+    m, v = distfn.stats(*arg)
+    check_cdf_ppf(distfn, arg, supp, distname + ' cdf_ppf')
+
+    check_pmf_cdf(distfn, arg, distname)
+    check_oth(distfn, arg, supp, distname + ' oth')
+    check_edge_support(distfn, arg)
+
+    alpha = 0.01
+    check_discrete_chisquare(distfn, arg, rvs, alpha,
+                             distname + ' chisquare')
+
+    if first_case:
+        locscale_defaults = (0,)
+        meths = [distfn.pmf, distfn.logpmf, distfn.cdf, distfn.logcdf,
+                 distfn.logsf]
+        # make sure arguments are within support
+        # for some distributions, this needs to be overridden
+        spec_k = {'randint': 11, 'hypergeom': 4, 'bernoulli': 0,
+                  'nchypergeom_wallenius': 6}
+        k = spec_k.get(distname, 1)
+        check_named_args(distfn, k, arg, locscale_defaults, meths)
+        if distname != 'sample distribution':
+            check_scale_docstring(distfn)
+        check_random_state_property(distfn, arg)
+        check_pickling(distfn, arg)
+        check_freezing(distfn, arg)
+
+        # Entropy
+        check_entropy(distfn, arg, distname)
+        if distfn.__class__._entropy != stats.rv_discrete._entropy:
+            check_private_entropy(distfn, arg, stats.rv_discrete)
+
+
+@pytest.mark.parametrize('distname,arg', distdiscrete)
+def test_moments(distname, arg):
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+        distname = 'sample distribution'
+    m, v, s, k = distfn.stats(*arg, moments='mvsk')
+    check_normalization(distfn, arg, distname)
+
+    # compare `stats` and `moment` methods
+    check_moment(distfn, arg, m, v, distname)
+    check_mean_expect(distfn, arg, m, distname)
+    check_var_expect(distfn, arg, m, v, distname)
+    check_skew_expect(distfn, arg, m, v, s, distname)
+    with np.testing.suppress_warnings() as sup:
+        if distname in ['zipf', 'betanbinom']:
+            sup.filter(RuntimeWarning)
+        check_kurt_expect(distfn, arg, m, v, k, distname)
+
+    # frozen distr moments
+    check_moment_frozen(distfn, arg, m, 1)
+    check_moment_frozen(distfn, arg, v+m*m, 2)
+
+
+@pytest.mark.parametrize('dist,shape_args', distdiscrete)
+def test_rvs_broadcast(dist, shape_args):
+    # If shape_only is True, it means the _rvs method of the
+    # distribution uses more than one random number to generate a random
+    # variate.  That means the result of using rvs with broadcasting or
+    # with a nontrivial size will not necessarily be the same as using the
+    # numpy.vectorize'd version of rvs(), so we can only compare the shapes
+    # of the results, not the values.
+    # Whether or not a distribution is in the following list is an
+    # implementation detail of the distribution, not a requirement.  If
+    # the implementation the rvs() method of a distribution changes, this
+    # test might also have to be changed.
+    shape_only = dist in ['betabinom', 'betanbinom', 'skellam', 'yulesimon',
+                          'dlaplace', 'nchypergeom_fisher',
+                          'nchypergeom_wallenius']
+
+    try:
+        distfunc = getattr(stats, dist)
+    except TypeError:
+        distfunc = dist
+        dist = f'rv_discrete(values=({dist.xk!r}, {dist.pk!r}))'
+    loc = np.zeros(2)
+    nargs = distfunc.numargs
+    allargs = []
+    bshape = []
+    # Generate shape parameter arguments...
+    for k in range(nargs):
+        shp = (k + 3,) + (1,)*(k + 1)
+        param_val = shape_args[k]
+        allargs.append(np.full(shp, param_val))
+        bshape.insert(0, shp[0])
+    allargs.append(loc)
+    bshape.append(loc.size)
+    # bshape holds the expected shape when loc, scale, and the shape
+    # parameters are all broadcast together.
+    check_rvs_broadcast(
+        distfunc, dist, allargs, bshape, shape_only, [np.dtype(int)]
+    )
+
+
+@pytest.mark.parametrize('dist,args', distdiscrete)
+def test_ppf_with_loc(dist, args):
+    try:
+        distfn = getattr(stats, dist)
+    except TypeError:
+        distfn = dist
+    #check with a negative, no and positive relocation.
+    np.random.seed(1942349)
+    re_locs = [np.random.randint(-10, -1), 0, np.random.randint(1, 10)]
+    _a, _b = distfn.support(*args)
+    for loc in re_locs:
+        npt.assert_array_equal(
+            [_a-1+loc, _b+loc],
+            [distfn.ppf(0.0, *args, loc=loc), distfn.ppf(1.0, *args, loc=loc)]
+            )
+
+
+@pytest.mark.parametrize('dist, args', distdiscrete)
+def test_isf_with_loc(dist, args):
+    try:
+        distfn = getattr(stats, dist)
+    except TypeError:
+        distfn = dist
+    # check with a negative, no and positive relocation.
+    np.random.seed(1942349)
+    re_locs = [np.random.randint(-10, -1), 0, np.random.randint(1, 10)]
+    _a, _b = distfn.support(*args)
+    for loc in re_locs:
+        expected = _b + loc, _a - 1 + loc
+        res = distfn.isf(0., *args, loc=loc), distfn.isf(1., *args, loc=loc)
+        npt.assert_array_equal(expected, res)
+    # test broadcasting behaviour
+    re_locs = [np.random.randint(-10, -1, size=(5, 3)),
+               np.zeros((5, 3)),
+               np.random.randint(1, 10, size=(5, 3))]
+    _a, _b = distfn.support(*args)
+    for loc in re_locs:
+        expected = _b + loc, _a - 1 + loc
+        res = distfn.isf(0., *args, loc=loc), distfn.isf(1., *args, loc=loc)
+        npt.assert_array_equal(expected, res)
+
+
+def check_cdf_ppf(distfn, arg, supp, msg):
+    # supp is assumed to be an array of integers in the support of distfn
+    # (but not necessarily all the integers in the support).
+    # This test assumes that the PMF of any value in the support of the
+    # distribution is greater than 1e-8.
+
+    # cdf is a step function, and ppf(q) = min{k : cdf(k) >= q, k integer}
+    cdf_supp = distfn.cdf(supp, *arg)
+    # In very rare cases, the finite precision calculation of ppf(cdf(supp))
+    # can produce an array in which an element is off by one.  We nudge the
+    # CDF values down by a few ULPs help to avoid this.
+    n_ulps = roundtrip_cdf_ppf_exceptions.get(distfn.name, 15)
+    cdf_supp0 = cdf_supp - n_ulps*np.spacing(cdf_supp)
+    npt.assert_array_equal(distfn.ppf(cdf_supp0, *arg),
+                           supp, msg + '-roundtrip')
+    # Repeat the same calculation, but with the CDF values decreased by 1e-8.
+    npt.assert_array_equal(distfn.ppf(distfn.cdf(supp, *arg) - 1e-8, *arg),
+                           supp, msg + '-roundtrip')
+
+    if not hasattr(distfn, 'xk'):
+        _a, _b = distfn.support(*arg)
+        supp1 = supp[supp < _b]
+        npt.assert_array_equal(distfn.ppf(distfn.cdf(supp1, *arg) + 1e-8, *arg),
+                               supp1 + distfn.inc, msg + ' ppf-cdf-next')
+
+
+def check_pmf_cdf(distfn, arg, distname):
+    if hasattr(distfn, 'xk'):
+        index = distfn.xk
+    else:
+        startind = int(distfn.ppf(0.01, *arg) - 1)
+        index = list(range(startind, startind + 10))
+    cdfs = distfn.cdf(index, *arg)
+    pmfs_cum = distfn.pmf(index, *arg).cumsum()
+
+    atol, rtol = 1e-10, 1e-10
+    if distname == 'skellam':    # ncx2 accuracy
+        atol, rtol = 1e-5, 1e-5
+    npt.assert_allclose(cdfs - cdfs[0], pmfs_cum - pmfs_cum[0],
+                        atol=atol, rtol=rtol)
+
+    # also check that pmf at non-integral k is zero
+    k = np.asarray(index)
+    k_shifted = k[:-1] + np.diff(k)/2
+    npt.assert_equal(distfn.pmf(k_shifted, *arg), 0)
+
+    # better check frozen distributions, and also when loc != 0
+    loc = 0.5
+    dist = distfn(loc=loc, *arg)
+    npt.assert_allclose(dist.pmf(k[1:] + loc), np.diff(dist.cdf(k + loc)))
+    npt.assert_equal(dist.pmf(k_shifted + loc), 0)
+
+
+def check_moment_frozen(distfn, arg, m, k):
+    npt.assert_allclose(distfn(*arg).moment(k), m,
+                        atol=1e-10, rtol=1e-10)
+
+
+def check_oth(distfn, arg, supp, msg):
+    # checking other methods of distfn
+    npt.assert_allclose(distfn.sf(supp, *arg), 1. - distfn.cdf(supp, *arg),
+                        atol=1e-10, rtol=1e-10)
+
+    q = np.linspace(0.01, 0.99, 20)
+    npt.assert_allclose(distfn.isf(q, *arg), distfn.ppf(1. - q, *arg),
+                        atol=1e-10, rtol=1e-10)
+
+    median_sf = distfn.isf(0.5, *arg)
+    npt.assert_(distfn.sf(median_sf - 1, *arg) > 0.5)
+    npt.assert_(distfn.cdf(median_sf + 1, *arg) > 0.5)
+
+
+def check_discrete_chisquare(distfn, arg, rvs, alpha, msg):
+    """Perform chisquare test for random sample of a discrete distribution
+
+    Parameters
+    ----------
+    distname : string
+        name of distribution function
+    arg : sequence
+        parameters of distribution
+    alpha : float
+        significance level, threshold for p-value
+
+    Returns
+    -------
+    result : bool
+        0 if test passes, 1 if test fails
+
+    """
+    wsupp = 0.05
+
+    # construct intervals with minimum mass `wsupp`.
+    # intervals are left-half-open as in a cdf difference
+    _a, _b = distfn.support(*arg)
+    lo = int(max(_a, -1000))
+    high = int(min(_b, 1000)) + 1
+    distsupport = range(lo, high)
+    last = 0
+    distsupp = [lo]
+    distmass = []
+    for ii in distsupport:
+        current = distfn.cdf(ii, *arg)
+        if current - last >= wsupp - 1e-14:
+            distsupp.append(ii)
+            distmass.append(current - last)
+            last = current
+            if current > (1 - wsupp):
+                break
+    if distsupp[-1] < _b:
+        distsupp.append(_b)
+        distmass.append(1 - last)
+    distsupp = np.array(distsupp)
+    distmass = np.array(distmass)
+
+    # convert intervals to right-half-open as required by histogram
+    histsupp = distsupp + 1e-8
+    histsupp[0] = _a
+
+    # find sample frequencies and perform chisquare test
+    freq, hsupp = np.histogram(rvs, histsupp)
+    chis, pval = stats.chisquare(np.array(freq), len(rvs)*distmass)
+
+    npt.assert_(
+        pval > alpha,
+        f'chisquare - test for {msg} at arg = {str(arg)} with pval = {str(pval)}'
+    )
+
+
+def check_scale_docstring(distfn):
+    if distfn.__doc__ is not None:
+        # Docstrings can be stripped if interpreter is run with -OO
+        npt.assert_('scale' not in distfn.__doc__)
+
+
+@pytest.mark.parametrize('method', ['pmf', 'logpmf', 'cdf', 'logcdf',
+                                    'sf', 'logsf', 'ppf', 'isf'])
+@pytest.mark.parametrize('distname, args', distdiscrete)
+def test_methods_with_lists(method, distname, args):
+    # Test that the discrete distributions can accept Python lists
+    # as arguments.
+    try:
+        dist = getattr(stats, distname)
+    except TypeError:
+        return
+    if method in ['ppf', 'isf']:
+        z = [0.1, 0.2]
+    else:
+        z = [0, 1]
+    p2 = [[p]*2 for p in args]
+    loc = [0, 1]
+    result = dist.pmf(z, *p2, loc=loc)
+    npt.assert_allclose(result,
+                        [dist.pmf(*v) for v in zip(z, *p2, loc)],
+                        rtol=1e-15, atol=1e-15)
+
+
+@pytest.mark.parametrize('distname, args', invdistdiscrete)
+def test_cdf_gh13280_regression(distname, args):
+    # Test for nan output when shape parameters are invalid
+    dist = getattr(stats, distname)
+    x = np.arange(-2, 15)
+    vals = dist.cdf(x, *args)
+    expected = np.nan
+    npt.assert_equal(vals, expected)
+
+
+def cases_test_discrete_integer_shapes():
+    # distributions parameters that are only allowed to be integral when
+    # fitting, but are allowed to be real as input to PDF, etc.
+    integrality_exceptions = {'nbinom': {'n'}, 'betanbinom': {'n'}}
+
+    seen = set()
+    for distname, shapes in distdiscrete:
+        if distname in seen:
+            continue
+        seen.add(distname)
+
+        try:
+            dist = getattr(stats, distname)
+        except TypeError:
+            continue
+
+        shape_info = dist._shape_info()
+
+        for i, shape in enumerate(shape_info):
+            if (shape.name in integrality_exceptions.get(distname, set()) or
+                    not shape.integrality):
+                continue
+
+            yield distname, shape.name, shapes
+
+
+@pytest.mark.parametrize('distname, shapename, shapes',
+                         cases_test_discrete_integer_shapes())
+def test_integer_shapes(distname, shapename, shapes):
+    dist = getattr(stats, distname)
+    shape_info = dist._shape_info()
+    shape_names = [shape.name for shape in shape_info]
+    i = shape_names.index(shapename)  # this element of params must be integral
+
+    shapes_copy = list(shapes)
+
+    valid_shape = shapes[i]
+    invalid_shape = valid_shape - 0.5  # arbitrary non-integral value
+    new_valid_shape = valid_shape - 1
+    shapes_copy[i] = [[valid_shape], [invalid_shape], [new_valid_shape]]
+
+    a, b = dist.support(*shapes)
+    x = np.round(np.linspace(a, b, 5))
+
+    pmf = dist.pmf(x, *shapes_copy)
+    assert not np.any(np.isnan(pmf[0, :]))
+    assert np.all(np.isnan(pmf[1, :]))
+    assert not np.any(np.isnan(pmf[2, :]))
+
+
+def test_frozen_attributes():
+    # gh-14827 reported that all frozen distributions had both pmf and pdf
+    # attributes; continuous should have pdf and discrete should have pmf.
+    message = "'rv_discrete_frozen' object has no attribute"
+    with pytest.raises(AttributeError, match=message):
+        stats.binom(10, 0.5).pdf
+    with pytest.raises(AttributeError, match=message):
+        stats.binom(10, 0.5).logpdf
+    stats.binom.pdf = "herring"
+    frozen_binom = stats.binom(10, 0.5)
+    assert isinstance(frozen_binom, rv_discrete_frozen)
+    delattr(stats.binom, 'pdf')
+
+
+@pytest.mark.parametrize('distname, shapes', distdiscrete)
+def test_interval(distname, shapes):
+    # gh-11026 reported that `interval` returns incorrect values when
+    # `confidence=1`. The values were not incorrect, but it was not intuitive
+    # that the left end of the interval should extend beyond the support of the
+    # distribution. Confirm that this is the behavior for all distributions.
+    if isinstance(distname, str):
+        dist = getattr(stats, distname)
+    else:
+        dist = distname
+    a, b = dist.support(*shapes)
+    npt.assert_equal(dist.ppf([0, 1], *shapes), (a-1, b))
+    npt.assert_equal(dist.isf([1, 0], *shapes), (a-1, b))
+    npt.assert_equal(dist.interval(1, *shapes), (a-1, b))
+
+
+@pytest.mark.xfail_on_32bit("Sensible to machine precision")
+def test_rv_sample():
+    # Thoroughly test rv_sample and check that gh-3758 is resolved
+
+    # Generate a random discrete distribution
+    rng = np.random.default_rng(98430143469)
+    xk = np.sort(rng.random(10) * 10)
+    pk = rng.random(10)
+    pk /= np.sum(pk)
+    dist = stats.rv_discrete(values=(xk, pk))
+
+    # Generate points to the left and right of xk
+    xk_left = (np.array([0] + xk[:-1].tolist()) + xk)/2
+    xk_right = (np.array(xk[1:].tolist() + [xk[-1]+1]) + xk)/2
+
+    # Generate points to the left and right of cdf
+    cdf2 = np.cumsum(pk)
+    cdf2_left = (np.array([0] + cdf2[:-1].tolist()) + cdf2)/2
+    cdf2_right = (np.array(cdf2[1:].tolist() + [1]) + cdf2)/2
+
+    # support - leftmost and rightmost xk
+    a, b = dist.support()
+    assert_allclose(a, xk[0])
+    assert_allclose(b, xk[-1])
+
+    # pmf - supported only on the xk
+    assert_allclose(dist.pmf(xk), pk)
+    assert_allclose(dist.pmf(xk_right), 0)
+    assert_allclose(dist.pmf(xk_left), 0)
+
+    # logpmf is log of the pmf; log(0) = -np.inf
+    with np.errstate(divide='ignore'):
+        assert_allclose(dist.logpmf(xk), np.log(pk))
+        assert_allclose(dist.logpmf(xk_right), -np.inf)
+        assert_allclose(dist.logpmf(xk_left), -np.inf)
+
+    # cdf - the cumulative sum of the pmf
+    assert_allclose(dist.cdf(xk), cdf2)
+    assert_allclose(dist.cdf(xk_right), cdf2)
+    assert_allclose(dist.cdf(xk_left), [0]+cdf2[:-1].tolist())
+
+    with np.errstate(divide='ignore'):
+        assert_allclose(dist.logcdf(xk), np.log(dist.cdf(xk)),
+                        atol=1e-15)
+        assert_allclose(dist.logcdf(xk_right), np.log(dist.cdf(xk_right)),
+                        atol=1e-15)
+        assert_allclose(dist.logcdf(xk_left), np.log(dist.cdf(xk_left)),
+                        atol=1e-15)
+
+    # sf is 1-cdf
+    assert_allclose(dist.sf(xk), 1-dist.cdf(xk))
+    assert_allclose(dist.sf(xk_right), 1-dist.cdf(xk_right))
+    assert_allclose(dist.sf(xk_left), 1-dist.cdf(xk_left))
+
+    with np.errstate(divide='ignore'):
+        assert_allclose(dist.logsf(xk), np.log(dist.sf(xk)),
+                        atol=1e-15)
+        assert_allclose(dist.logsf(xk_right), np.log(dist.sf(xk_right)),
+                        atol=1e-15)
+        assert_allclose(dist.logsf(xk_left), np.log(dist.sf(xk_left)),
+                        atol=1e-15)
+
+    # ppf
+    assert_allclose(dist.ppf(cdf2), xk)
+    assert_allclose(dist.ppf(cdf2_left), xk)
+    assert_allclose(dist.ppf(cdf2_right)[:-1], xk[1:])
+    assert_allclose(dist.ppf(0), a - 1)
+    assert_allclose(dist.ppf(1), b)
+
+    # isf
+    sf2 = dist.sf(xk)
+    assert_allclose(dist.isf(sf2), xk)
+    assert_allclose(dist.isf(1-cdf2_left), dist.ppf(cdf2_left))
+    assert_allclose(dist.isf(1-cdf2_right), dist.ppf(cdf2_right))
+    assert_allclose(dist.isf(0), b)
+    assert_allclose(dist.isf(1), a - 1)
+
+    # interval is (ppf(alpha/2), isf(alpha/2))
+    ps = np.linspace(0.01, 0.99, 10)
+    int2 = dist.ppf(ps/2), dist.isf(ps/2)
+    assert_allclose(dist.interval(1-ps), int2)
+    assert_allclose(dist.interval(0), dist.median())
+    assert_allclose(dist.interval(1), (a-1, b))
+
+    # median is simply ppf(0.5)
+    med2 = dist.ppf(0.5)
+    assert_allclose(dist.median(), med2)
+
+    # all four stats (mean, var, skew, and kurtosis) from the definitions
+    mean2 = np.sum(xk*pk)
+    var2 = np.sum((xk - mean2)**2 * pk)
+    skew2 = np.sum((xk - mean2)**3 * pk) / var2**(3/2)
+    kurt2 = np.sum((xk - mean2)**4 * pk) / var2**2 - 3
+    assert_allclose(dist.mean(), mean2)
+    assert_allclose(dist.std(), np.sqrt(var2))
+    assert_allclose(dist.var(), var2)
+    assert_allclose(dist.stats(moments='mvsk'), (mean2, var2, skew2, kurt2))
+
+    # noncentral moment against definition
+    mom3 = np.sum((xk**3) * pk)
+    assert_allclose(dist.moment(3), mom3)
+
+    # expect - check against moments
+    assert_allclose(dist.expect(lambda x: 1), 1)
+    assert_allclose(dist.expect(), mean2)
+    assert_allclose(dist.expect(lambda x: x**3), mom3)
+
+    # entropy is the negative of the expected value of log(p)
+    with np.errstate(divide='ignore'):
+        assert_allclose(-dist.expect(lambda x: dist.logpmf(x)), dist.entropy())
+
+    # RVS is just ppf of uniform random variates
+    rng = np.random.default_rng(98430143469)
+    rvs = dist.rvs(size=100, random_state=rng)
+    rng = np.random.default_rng(98430143469)
+    rvs0 = dist.ppf(rng.random(size=100))
+    assert_allclose(rvs, rvs0)
+
+def test__pmf_float_input():
+    # gh-21272
+    # test that `rvs()` can be computed when `_pmf` requires float input
+    
+    class rv_exponential(stats.rv_discrete):
+        def _pmf(self, i):
+            return (2/3)*3**(1 - i)
+    
+    rv = rv_exponential(a=0.0, b=float('inf'))
+    rvs = rv.rvs(random_state=42)  # should not crash due to integer input to `_pmf`
+    assert_allclose(rvs, 0)

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_discrete_distns.py

@@ -0,0 +1,648 @@
+import pytest
+import itertools
+
+from scipy.stats import (betabinom, betanbinom, hypergeom, nhypergeom,
+                         bernoulli, boltzmann, skellam, zipf, zipfian, binom,
+                         nbinom, nchypergeom_fisher, nchypergeom_wallenius,
+                         randint)
+
+import numpy as np
+from numpy.testing import (
+    assert_almost_equal, assert_equal, assert_allclose, suppress_warnings
+)
+from scipy.special import binom as special_binom
+from scipy.optimize import root_scalar
+from scipy.integrate import quad
+
+
+# The expected values were computed with Wolfram Alpha, using
+# the expression CDF[HypergeometricDistribution[N, n, M], k].
+@pytest.mark.parametrize('k, M, n, N, expected, rtol',
+                         [(3, 10, 4, 5,
+                           0.9761904761904762, 1e-15),
+                          (107, 10000, 3000, 215,
+                           0.9999999997226765, 1e-15),
+                          (10, 10000, 3000, 215,
+                           2.681682217692179e-21, 5e-11)])
+def test_hypergeom_cdf(k, M, n, N, expected, rtol):
+    p = hypergeom.cdf(k, M, n, N)
+    assert_allclose(p, expected, rtol=rtol)
+
+
+# The expected values were computed with Wolfram Alpha, using
+# the expression SurvivalFunction[HypergeometricDistribution[N, n, M], k].
+@pytest.mark.parametrize('k, M, n, N, expected, rtol',
+                         [(25, 10000, 3000, 215,
+                           0.9999999999052958, 1e-15),
+                          (125, 10000, 3000, 215,
+                           1.4416781705752128e-18, 5e-11)])
+def test_hypergeom_sf(k, M, n, N, expected, rtol):
+    p = hypergeom.sf(k, M, n, N)
+    assert_allclose(p, expected, rtol=rtol)
+
+
+def test_hypergeom_logpmf():
+    # symmetries test
+    # f(k,N,K,n) = f(n-k,N,N-K,n) = f(K-k,N,K,N-n) = f(k,N,n,K)
+    k = 5
+    N = 50
+    K = 10
+    n = 5
+    logpmf1 = hypergeom.logpmf(k, N, K, n)
+    logpmf2 = hypergeom.logpmf(n - k, N, N - K, n)
+    logpmf3 = hypergeom.logpmf(K - k, N, K, N - n)
+    logpmf4 = hypergeom.logpmf(k, N, n, K)
+    assert_almost_equal(logpmf1, logpmf2, decimal=12)
+    assert_almost_equal(logpmf1, logpmf3, decimal=12)
+    assert_almost_equal(logpmf1, logpmf4, decimal=12)
+
+    # test related distribution
+    # Bernoulli distribution if n = 1
+    k = 1
+    N = 10
+    K = 7
+    n = 1
+    hypergeom_logpmf = hypergeom.logpmf(k, N, K, n)
+    bernoulli_logpmf = bernoulli.logpmf(k, K/N)
+    assert_almost_equal(hypergeom_logpmf, bernoulli_logpmf, decimal=12)
+
+
+def test_nhypergeom_pmf():
+    # test with hypergeom
+    M, n, r = 45, 13, 8
+    k = 6
+    NHG = nhypergeom.pmf(k, M, n, r)
+    HG = hypergeom.pmf(k, M, n, k+r-1) * (M - n - (r-1)) / (M - (k+r-1))
+    assert_allclose(HG, NHG, rtol=1e-10)
+
+
+def test_nhypergeom_pmfcdf():
+    # test pmf and cdf with arbitrary values.
+    M = 8
+    n = 3
+    r = 4
+    support = np.arange(n+1)
+    pmf = nhypergeom.pmf(support, M, n, r)
+    cdf = nhypergeom.cdf(support, M, n, r)
+    assert_allclose(pmf, [1/14, 3/14, 5/14, 5/14], rtol=1e-13)
+    assert_allclose(cdf, [1/14, 4/14, 9/14, 1.0], rtol=1e-13)
+
+
+def test_nhypergeom_r0():
+    # test with `r = 0`.
+    M = 10
+    n = 3
+    r = 0
+    pmf = nhypergeom.pmf([[0, 1, 2, 0], [1, 2, 0, 3]], M, n, r)
+    assert_allclose(pmf, [[1, 0, 0, 1], [0, 0, 1, 0]], rtol=1e-13)
+
+
+def test_nhypergeom_rvs_shape():
+    # Check that when given a size with more dimensions than the
+    # dimensions of the broadcast parameters, rvs returns an array
+    # with the correct shape.
+    x = nhypergeom.rvs(22, [7, 8, 9], [[12], [13]], size=(5, 1, 2, 3))
+    assert x.shape == (5, 1, 2, 3)
+
+
+def test_nhypergeom_accuracy():
+    # Check that nhypergeom.rvs post-gh-13431 gives the same values as
+    # inverse transform sampling
+    np.random.seed(0)
+    x = nhypergeom.rvs(22, 7, 11, size=100)
+    np.random.seed(0)
+    p = np.random.uniform(size=100)
+    y = nhypergeom.ppf(p, 22, 7, 11)
+    assert_equal(x, y)
+
+
+def test_boltzmann_upper_bound():
+    k = np.arange(-3, 5)
+
+    N = 1
+    p = boltzmann.pmf(k, 0.123, N)
+    expected = k == 0
+    assert_equal(p, expected)
+
+    lam = np.log(2)
+    N = 3
+    p = boltzmann.pmf(k, lam, N)
+    expected = [0, 0, 0, 4/7, 2/7, 1/7, 0, 0]
+    assert_allclose(p, expected, rtol=1e-13)
+
+    c = boltzmann.cdf(k, lam, N)
+    expected = [0, 0, 0, 4/7, 6/7, 1, 1, 1]
+    assert_allclose(c, expected, rtol=1e-13)
+
+
+def test_betabinom_a_and_b_unity():
+    # test limiting case that betabinom(n, 1, 1) is a discrete uniform
+    # distribution from 0 to n
+    n = 20
+    k = np.arange(n + 1)
+    p = betabinom(n, 1, 1).pmf(k)
+    expected = np.repeat(1 / (n + 1), n + 1)
+    assert_almost_equal(p, expected)
+
+
+@pytest.mark.parametrize('dtypes', itertools.product(*[(int, float)]*3))
+def test_betabinom_stats_a_and_b_integers_gh18026(dtypes):
+    # gh-18026 reported that `betabinom` kurtosis calculation fails when some
+    # parameters are integers. Check that this is resolved.
+    n_type, a_type, b_type = dtypes
+    n, a, b = n_type(10), a_type(2), b_type(3)
+    assert_allclose(betabinom.stats(n, a, b, moments='k'), -0.6904761904761907)
+
+
+def test_betabinom_bernoulli():
+    # test limiting case that betabinom(1, a, b) = bernoulli(a / (a + b))
+    a = 2.3
+    b = 0.63
+    k = np.arange(2)
+    p = betabinom(1, a, b).pmf(k)
+    expected = bernoulli(a / (a + b)).pmf(k)
+    assert_almost_equal(p, expected)
+
+
+def test_issue_10317():
+    alpha, n, p = 0.9, 10, 1
+    assert_equal(nbinom.interval(confidence=alpha, n=n, p=p), (0, 0))
+
+
+def test_issue_11134():
+    alpha, n, p = 0.95, 10, 0
+    assert_equal(binom.interval(confidence=alpha, n=n, p=p), (0, 0))
+
+
+def test_issue_7406():
+    np.random.seed(0)
+    assert_equal(binom.ppf(np.random.rand(10), 0, 0.5), 0)
+
+    # Also check that endpoints (q=0, q=1) are correct
+    assert_equal(binom.ppf(0, 0, 0.5), -1)
+    assert_equal(binom.ppf(1, 0, 0.5), 0)
+
+
+def test_issue_5122():
+    p = 0
+    n = np.random.randint(100, size=10)
+
+    x = 0
+    ppf = binom.ppf(x, n, p)
+    assert_equal(ppf, -1)
+
+    x = np.linspace(0.01, 0.99, 10)
+    ppf = binom.ppf(x, n, p)
+    assert_equal(ppf, 0)
+
+    x = 1
+    ppf = binom.ppf(x, n, p)
+    assert_equal(ppf, n)
+
+
+def test_issue_1603():
+    assert_equal(binom(1000, np.logspace(-3, -100)).ppf(0.01), 0)
+
+
+def test_issue_5503():
+    p = 0.5
+    x = np.logspace(3, 14, 12)
+    assert_allclose(binom.cdf(x, 2*x, p), 0.5, atol=1e-2)
+
+
+@pytest.mark.parametrize('x, n, p, cdf_desired', [
+    (300, 1000, 3/10, 0.51559351981411995636),
+    (3000, 10000, 3/10, 0.50493298381929698016),
+    (30000, 100000, 3/10, 0.50156000591726422864),
+    (300000, 1000000, 3/10, 0.50049331906666960038),
+    (3000000, 10000000, 3/10, 0.50015600124585261196),
+    (30000000, 100000000, 3/10, 0.50004933192735230102),
+    (30010000, 100000000, 3/10, 0.98545384016570790717),
+    (29990000, 100000000, 3/10, 0.01455017177985268670),
+    (29950000, 100000000, 3/10, 5.02250963487432024943e-28),
+])
+def test_issue_5503pt2(x, n, p, cdf_desired):
+    assert_allclose(binom.cdf(x, n, p), cdf_desired)
+
+
+def test_issue_5503pt3():
+    # From Wolfram Alpha: CDF[BinomialDistribution[1e12, 1e-12], 2]
+    assert_allclose(binom.cdf(2, 10**12, 10**-12), 0.91969860292869777384)
+
+
+def test_issue_6682():
+    # Reference value from R:
+    # options(digits=16)
+    # print(pnbinom(250, 50, 32/63, lower.tail=FALSE))
+    assert_allclose(nbinom.sf(250, 50, 32./63.), 1.460458510976452e-35)
+
+
+def test_issue_19747():
+    # test that negative k does not raise an error in nbinom.logcdf
+    result = nbinom.logcdf([5, -1, 1], 5, 0.5)
+    reference = [-0.47313352, -np.inf, -2.21297293]
+    assert_allclose(result, reference)
+
+
+def test_boost_divide_by_zero_issue_15101():
+    n = 1000
+    p = 0.01
+    k = 996
+    assert_allclose(binom.pmf(k, n, p), 0.0)
+
+
+def test_skellam_gh11474():
+    # test issue reported in gh-11474 caused by `cdfchn`
+    mu = [1, 10, 100, 1000, 5000, 5050, 5100, 5250, 6000]
+    cdf = skellam.cdf(0, mu, mu)
+    # generated in R
+    # library(skellam)
+    # options(digits = 16)
+    # mu = c(1, 10, 100, 1000, 5000, 5050, 5100, 5250, 6000)
+    # pskellam(0, mu, mu, TRUE)
+    cdf_expected = [0.6542541612768356, 0.5448901559424127, 0.5141135799745580,
+                    0.5044605891382528, 0.5019947363350450, 0.5019848365953181,
+                    0.5019750827993392, 0.5019466621805060, 0.5018209330219539]
+    assert_allclose(cdf, cdf_expected)
+
+
+class TestZipfian:
+    def test_zipfian_asymptotic(self):
+        # test limiting case that zipfian(a, n) -> zipf(a) as n-> oo
+        a = 6.5
+        N = 10000000
+        k = np.arange(1, 21)
+        assert_allclose(zipfian.pmf(k, a, N), zipf.pmf(k, a))
+        assert_allclose(zipfian.cdf(k, a, N), zipf.cdf(k, a))
+        assert_allclose(zipfian.sf(k, a, N), zipf.sf(k, a))
+        assert_allclose(zipfian.stats(a, N, moments='msvk'),
+                        zipf.stats(a, moments='msvk'))
+
+    def test_zipfian_continuity(self):
+        # test that zipfian(0.999999, n) ~ zipfian(1.000001, n)
+        # (a = 1 switches between methods of calculating harmonic sum)
+        alt1, agt1 = 0.99999999, 1.00000001
+        N = 30
+        k = np.arange(1, N + 1)
+        assert_allclose(zipfian.pmf(k, alt1, N), zipfian.pmf(k, agt1, N),
+                        rtol=5e-7)
+        assert_allclose(zipfian.cdf(k, alt1, N), zipfian.cdf(k, agt1, N),
+                        rtol=5e-7)
+        assert_allclose(zipfian.sf(k, alt1, N), zipfian.sf(k, agt1, N),
+                        rtol=5e-7)
+        assert_allclose(zipfian.stats(alt1, N, moments='msvk'),
+                        zipfian.stats(agt1, N, moments='msvk'), rtol=5e-7)
+
+    def test_zipfian_R(self):
+        # test against R VGAM package
+        # library(VGAM)
+        # k <- c(13, 16,  1,  4,  4,  8, 10, 19,  5,  7)
+        # a <- c(1.56712977, 3.72656295, 5.77665117, 9.12168729, 5.79977172,
+        #        4.92784796, 9.36078764, 4.3739616 , 7.48171872, 4.6824154)
+        # n <- c(70, 80, 48, 65, 83, 89, 50, 30, 20, 20)
+        # pmf <- dzipf(k, N = n, shape = a)
+        # cdf <- pzipf(k, N = n, shape = a)
+        # print(pmf)
+        # print(cdf)
+        np.random.seed(0)
+        k = np.random.randint(1, 20, size=10)
+        a = np.random.rand(10)*10 + 1
+        n = np.random.randint(1, 100, size=10)
+        pmf = [8.076972e-03, 2.950214e-05, 9.799333e-01, 3.216601e-06,
+               3.158895e-04, 3.412497e-05, 4.350472e-10, 2.405773e-06,
+               5.860662e-06, 1.053948e-04]
+        cdf = [0.8964133, 0.9998666, 0.9799333, 0.9999995, 0.9998584,
+               0.9999458, 1.0000000, 0.9999920, 0.9999977, 0.9998498]
+        # skip the first point; zipUC is not accurate for low a, n
+        assert_allclose(zipfian.pmf(k, a, n)[1:], pmf[1:], rtol=1e-6)
+        assert_allclose(zipfian.cdf(k, a, n)[1:], cdf[1:], rtol=5e-5)
+
+    np.random.seed(0)
+    naive_tests = np.vstack((np.logspace(-2, 1, 10),
+                             np.random.randint(2, 40, 10))).T
+
+    @pytest.mark.parametrize("a, n", naive_tests)
+    def test_zipfian_naive(self, a, n):
+        # test against bare-bones implementation
+
+        @np.vectorize
+        def Hns(n, s):
+            """Naive implementation of harmonic sum"""
+            return (1/np.arange(1, n+1)**s).sum()
+
+        @np.vectorize
+        def pzip(k, a, n):
+            """Naive implementation of zipfian pmf"""
+            if k < 1 or k > n:
+                return 0.
+            else:
+                return 1 / k**a / Hns(n, a)
+
+        k = np.arange(n+1)
+        pmf = pzip(k, a, n)
+        cdf = np.cumsum(pmf)
+        mean = np.average(k, weights=pmf)
+        var = np.average((k - mean)**2, weights=pmf)
+        std = var**0.5
+        skew = np.average(((k-mean)/std)**3, weights=pmf)
+        kurtosis = np.average(((k-mean)/std)**4, weights=pmf) - 3
+        assert_allclose(zipfian.pmf(k, a, n), pmf)
+        assert_allclose(zipfian.cdf(k, a, n), cdf)
+        assert_allclose(zipfian.stats(a, n, moments="mvsk"),
+                        [mean, var, skew, kurtosis])
+
+    def test_pmf_integer_k(self):
+        k = np.arange(0, 1000)
+        k_int32 = k.astype(np.int32)
+        dist = zipfian(111, 22)
+        pmf = dist.pmf(k)
+        pmf_k_int32 = dist.pmf(k_int32)
+        assert_equal(pmf, pmf_k_int32)
+
+
+class TestNCH:
+    np.random.seed(2)  # seeds 0 and 1 had some xl = xu; randint failed
+    shape = (2, 4, 3)
+    max_m = 100
+    m1 = np.random.randint(1, max_m, size=shape)    # red balls
+    m2 = np.random.randint(1, max_m, size=shape)    # white balls
+    N = m1 + m2                                     # total balls
+    n = randint.rvs(0, N, size=N.shape)             # number of draws
+    xl = np.maximum(0, n-m2)                        # lower bound of support
+    xu = np.minimum(n, m1)                          # upper bound of support
+    x = randint.rvs(xl, xu, size=xl.shape)
+    odds = np.random.rand(*x.shape)*2
+
+    # test output is more readable when function names (strings) are passed
+    @pytest.mark.parametrize('dist_name',
+                             ['nchypergeom_fisher', 'nchypergeom_wallenius'])
+    def test_nch_hypergeom(self, dist_name):
+        # Both noncentral hypergeometric distributions reduce to the
+        # hypergeometric distribution when odds = 1
+        dists = {'nchypergeom_fisher': nchypergeom_fisher,
+                 'nchypergeom_wallenius': nchypergeom_wallenius}
+        dist = dists[dist_name]
+        x, N, m1, n = self.x, self.N, self.m1, self.n
+        assert_allclose(dist.pmf(x, N, m1, n, odds=1),
+                        hypergeom.pmf(x, N, m1, n))
+
+    def test_nchypergeom_fisher_naive(self):
+        # test against a very simple implementation
+        x, N, m1, n, odds = self.x, self.N, self.m1, self.n, self.odds
+
+        @np.vectorize
+        def pmf_mean_var(x, N, m1, n, w):
+            # simple implementation of nchypergeom_fisher pmf
+            m2 = N - m1
+            xl = np.maximum(0, n-m2)
+            xu = np.minimum(n, m1)
+
+            def f(x):
+                t1 = special_binom(m1, x)
+                t2 = special_binom(m2, n - x)
+                return t1 * t2 * w**x
+
+            def P(k):
+                return sum(f(y)*y**k for y in range(xl, xu + 1))
+
+            P0 = P(0)
+            P1 = P(1)
+            P2 = P(2)
+            pmf = f(x) / P0
+            mean = P1 / P0
+            var = P2 / P0 - (P1 / P0)**2
+            return pmf, mean, var
+
+        pmf, mean, var = pmf_mean_var(x, N, m1, n, odds)
+        assert_allclose(nchypergeom_fisher.pmf(x, N, m1, n, odds), pmf)
+        assert_allclose(nchypergeom_fisher.stats(N, m1, n, odds, moments='m'),
+                        mean)
+        assert_allclose(nchypergeom_fisher.stats(N, m1, n, odds, moments='v'),
+                        var)
+
+    def test_nchypergeom_wallenius_naive(self):
+        # test against a very simple implementation
+
+        np.random.seed(2)
+        shape = (2, 4, 3)
+        max_m = 100
+        m1 = np.random.randint(1, max_m, size=shape)
+        m2 = np.random.randint(1, max_m, size=shape)
+        N = m1 + m2
+        n = randint.rvs(0, N, size=N.shape)
+        xl = np.maximum(0, n-m2)
+        xu = np.minimum(n, m1)
+        x = randint.rvs(xl, xu, size=xl.shape)
+        w = np.random.rand(*x.shape)*2
+
+        def support(N, m1, n, w):
+            m2 = N - m1
+            xl = np.maximum(0, n-m2)
+            xu = np.minimum(n, m1)
+            return xl, xu
+
+        @np.vectorize
+        def mean(N, m1, n, w):
+            m2 = N - m1
+            xl, xu = support(N, m1, n, w)
+
+            def fun(u):
+                return u/m1 + (1 - (n-u)/m2)**w - 1
+
+            return root_scalar(fun, bracket=(xl, xu)).root
+
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning,
+                       message="invalid value encountered in mean")
+            assert_allclose(nchypergeom_wallenius.mean(N, m1, n, w),
+                            mean(N, m1, n, w), rtol=2e-2)
+
+        @np.vectorize
+        def variance(N, m1, n, w):
+            m2 = N - m1
+            u = mean(N, m1, n, w)
+            a = u * (m1 - u)
+            b = (n-u)*(u + m2 - n)
+            return N*a*b / ((N-1) * (m1*b + m2*a))
+
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning,
+                       message="invalid value encountered in mean")
+            assert_allclose(
+                nchypergeom_wallenius.stats(N, m1, n, w, moments='v'),
+                variance(N, m1, n, w),
+                rtol=5e-2
+            )
+
+        @np.vectorize
+        def pmf(x, N, m1, n, w):
+            m2 = N - m1
+            xl, xu = support(N, m1, n, w)
+
+            def integrand(t):
+                D = w*(m1 - x) + (m2 - (n-x))
+                res = (1-t**(w/D))**x * (1-t**(1/D))**(n-x)
+                return res
+
+            def f(x):
+                t1 = special_binom(m1, x)
+                t2 = special_binom(m2, n - x)
+                the_integral = quad(integrand, 0, 1,
+                                    epsrel=1e-16, epsabs=1e-16)
+                return t1 * t2 * the_integral[0]
+
+            return f(x)
+
+        pmf0 = pmf(x, N, m1, n, w)
+        pmf1 = nchypergeom_wallenius.pmf(x, N, m1, n, w)
+
+        atol, rtol = 1e-6, 1e-6
+        i = np.abs(pmf1 - pmf0) < atol + rtol*np.abs(pmf0)
+        assert i.sum() > np.prod(shape) / 2  # works at least half the time
+
+        # for those that fail, discredit the naive implementation
+        for N, m1, n, w in zip(N[~i], m1[~i], n[~i], w[~i]):
+            # get the support
+            m2 = N - m1
+            xl, xu = support(N, m1, n, w)
+            x = np.arange(xl, xu + 1)
+
+            # calculate sum of pmf over the support
+            # the naive implementation is very wrong in these cases
+            assert pmf(x, N, m1, n, w).sum() < .5
+            assert_allclose(nchypergeom_wallenius.pmf(x, N, m1, n, w).sum(), 1)
+
+    def test_wallenius_against_mpmath(self):
+        # precompute data with mpmath since naive implementation above
+        # is not reliable. See source code in gh-13330.
+        M = 50
+        n = 30
+        N = 20
+        odds = 2.25
+        # Expected results, computed with mpmath.
+        sup = np.arange(21)
+        pmf = np.array([3.699003068656875e-20,
+                        5.89398584245431e-17,
+                        2.1594437742911123e-14,
+                        3.221458044649955e-12,
+                        2.4658279241205077e-10,
+                        1.0965862603981212e-08,
+                        3.057890479665704e-07,
+                        5.622818831643761e-06,
+                        7.056482841531681e-05,
+                        0.000618899425358671,
+                        0.003854172932571669,
+                        0.01720592676256026,
+                        0.05528844897093792,
+                        0.12772363313574242,
+                        0.21065898367825722,
+                        0.24465958845359234,
+                        0.1955114898110033,
+                        0.10355390084949237,
+                        0.03414490375225675,
+                        0.006231989845775931,
+                        0.0004715577304677075])
+        mean = 14.808018384813426
+        var = 2.6085975877923717
+
+        # nchypergeom_wallenius.pmf returns 0 for pmf(0) and pmf(1), and pmf(2)
+        # has only three digits of accuracy (~ 2.1511e-14).
+        assert_allclose(nchypergeom_wallenius.pmf(sup, M, n, N, odds), pmf,
+                        rtol=1e-13, atol=1e-13)
+        assert_allclose(nchypergeom_wallenius.mean(M, n, N, odds),
+                        mean, rtol=1e-13)
+        assert_allclose(nchypergeom_wallenius.var(M, n, N, odds),
+                        var, rtol=1e-11)
+
+    @pytest.mark.parametrize('dist_name',
+                             ['nchypergeom_fisher', 'nchypergeom_wallenius'])
+    def test_rvs_shape(self, dist_name):
+        # Check that when given a size with more dimensions than the
+        # dimensions of the broadcast parameters, rvs returns an array
+        # with the correct shape.
+        dists = {'nchypergeom_fisher': nchypergeom_fisher,
+                 'nchypergeom_wallenius': nchypergeom_wallenius}
+        dist = dists[dist_name]
+        x = dist.rvs(50, 30, [[10], [20]], [0.5, 1.0, 2.0], size=(5, 1, 2, 3))
+        assert x.shape == (5, 1, 2, 3)
+
+
+@pytest.mark.parametrize("mu, q, expected",
+                         [[10, 120, -1.240089881791596e-38],
+                          [1500, 0, -86.61466680572661]])
+def test_nbinom_11465(mu, q, expected):
+    # test nbinom.logcdf at extreme tails
+    size = 20
+    n, p = size, size/(size+mu)
+    # In R:
+    # options(digits=16)
+    # pnbinom(mu=10, size=20, q=120, log.p=TRUE)
+    assert_allclose(nbinom.logcdf(q, n, p), expected)
+
+
+def test_gh_17146():
+    # Check that discrete distributions return PMF of zero at non-integral x.
+    # See gh-17146.
+    x = np.linspace(0, 1, 11)
+    p = 0.8
+    pmf = bernoulli(p).pmf(x)
+    i = (x % 1 == 0)
+    assert_allclose(pmf[-1], p)
+    assert_allclose(pmf[0], 1-p)
+    assert_equal(pmf[~i], 0)
+
+
+class TestBetaNBinom:
+    @pytest.mark.parametrize('x, n, a, b, ref',
+                            [[5, 5e6, 5, 20, 1.1520944824139114e-107],
+                            [100, 50, 5, 20, 0.002855762954310226],
+                            [10000, 1000, 5, 20, 1.9648515726019154e-05]])
+    def test_betanbinom_pmf(self, x, n, a, b, ref):
+        # test that PMF stays accurate in the distribution tails
+        # reference values computed with mpmath
+        # from mpmath import mp
+        # mp.dps = 500
+        # def betanbinom_pmf(k, n, a, b):
+        #     k = mp.mpf(k)
+        #     a = mp.mpf(a)
+        #     b = mp.mpf(b)
+        #     n = mp.mpf(n)
+        #     return float(mp.binomial(n + k - mp.one, k)
+        #                  * mp.beta(a + n, b + k) / mp.beta(a, b))
+        assert_allclose(betanbinom.pmf(x, n, a, b), ref, rtol=1e-10)
+
+
+    @pytest.mark.parametrize('n, a, b, ref',
+                            [[10000, 5000, 50, 0.12841520515722202],
+                            [10, 9, 9, 7.9224400871459695],
+                            [100, 1000, 10, 1.5849602176622748]])
+    def test_betanbinom_kurtosis(self, n, a, b, ref):
+        # reference values were computed via mpmath
+        # from mpmath import mp
+        # def kurtosis_betanegbinom(n, a, b):
+        #     n = mp.mpf(n)
+        #     a = mp.mpf(a)
+        #     b = mp.mpf(b)
+        #     four = mp.mpf(4.)
+        #     mean = n * b / (a - mp.one)
+        #     var = (n * b * (n + a - 1.) * (a + b - 1.)
+        #            / ((a - 2.) * (a - 1.)**2.))
+        #     def f(k):
+        #         return (mp.binomial(n + k - mp.one, k)
+        #                 * mp.beta(a + n, b + k) / mp.beta(a, b)
+        #                 * (k - mean)**four)
+        #      fourth_moment = mp.nsum(f, [0, mp.inf])
+        #      return float(fourth_moment/var**2 - 3.)
+        assert_allclose(betanbinom.stats(n, a, b, moments="k"),
+                        ref, rtol=3e-15)
+
+
+class TestZipf:
+    def test_gh20692(self):
+        # test that int32 data for k generates same output as double
+        k = np.arange(0, 1000)
+        k_int32 = k.astype(np.int32)
+        dist = zipf(9)
+        pmf = dist.pmf(k)
+        pmf_k_int32 = dist.pmf(k_int32)
+        assert_equal(pmf, pmf_k_int32)

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_entropy.py

@@ -0,0 +1,304 @@
+import math
+import pytest
+from pytest import raises as assert_raises
+
+import numpy as np
+from numpy.testing import assert_allclose
+
+from scipy import stats
+from scipy.conftest import array_api_compatible
+from scipy._lib._array_api import xp_assert_close, xp_assert_equal, xp_assert_less
+
+class TestEntropy:
+    @array_api_compatible
+    def test_entropy_positive(self, xp):
+        # See ticket #497
+        pk = xp.asarray([0.5, 0.2, 0.3])
+        qk = xp.asarray([0.1, 0.25, 0.65])
+        eself = stats.entropy(pk, pk)
+        edouble = stats.entropy(pk, qk)
+        xp_assert_equal(eself, xp.asarray(0.))
+        xp_assert_less(-edouble, xp.asarray(0.))
+
+    @array_api_compatible
+    def test_entropy_base(self, xp):
+        pk = xp.ones(16)
+        S = stats.entropy(pk, base=2.)
+        xp_assert_less(xp.abs(S - 4.), xp.asarray(1.e-5))
+
+        qk = xp.ones(16)
+        qk = xp.where(xp.arange(16) < 8, xp.asarray(2.), qk)
+        S = stats.entropy(pk, qk)
+        S2 = stats.entropy(pk, qk, base=2.)
+        xp_assert_less(xp.abs(S/S2 - math.log(2.)), xp.asarray(1.e-5))
+
+    @array_api_compatible
+    def test_entropy_zero(self, xp):
+        # Test for PR-479
+        x = xp.asarray([0., 1., 2.])
+        xp_assert_close(stats.entropy(x),
+                        xp.asarray(0.63651416829481278))
+
+    @array_api_compatible
+    def test_entropy_2d(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        qk = xp.asarray([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
+        xp_assert_close(stats.entropy(pk, qk),
+                        xp.asarray([0.1933259, 0.18609809]))
+
+    @array_api_compatible
+    def test_entropy_2d_zero(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        qk = xp.asarray([[0.0, 0.1], [0.3, 0.6], [0.5, 0.3]])
+        xp_assert_close(stats.entropy(pk, qk),
+                        xp.asarray([xp.inf, 0.18609809]))
+
+        pk = xp.asarray([[0.0, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        xp_assert_close(stats.entropy(pk, qk),
+                        xp.asarray([0.17403988, 0.18609809]))
+
+    @array_api_compatible
+    def test_entropy_base_2d_nondefault_axis(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        xp_assert_close(stats.entropy(pk, axis=1),
+                        xp.asarray([0.63651417, 0.63651417, 0.66156324]))
+
+    @array_api_compatible
+    def test_entropy_2d_nondefault_axis(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        qk = xp.asarray([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
+        xp_assert_close(stats.entropy(pk, qk, axis=1),
+                        xp.asarray([0.23104906, 0.23104906, 0.12770641]))
+
+    @array_api_compatible
+    def test_entropy_raises_value_error(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        qk = xp.asarray([[0.1, 0.2], [0.6, 0.3]])
+        message = "Array shapes are incompatible for broadcasting."
+        with pytest.raises(ValueError, match=message):
+            stats.entropy(pk, qk)
+
+    @array_api_compatible
+    def test_base_entropy_with_axis_0_is_equal_to_default(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        xp_assert_close(stats.entropy(pk, axis=0),
+                        stats.entropy(pk))
+
+    @array_api_compatible
+    def test_entropy_with_axis_0_is_equal_to_default(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        qk = xp.asarray([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
+        xp_assert_close(stats.entropy(pk, qk, axis=0),
+                        stats.entropy(pk, qk))
+
+    @array_api_compatible
+    def test_base_entropy_transposed(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        xp_assert_close(stats.entropy(pk.T),
+                        stats.entropy(pk, axis=1))
+
+    @array_api_compatible
+    def test_entropy_transposed(self, xp):
+        pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        qk = xp.asarray([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
+        xp_assert_close(stats.entropy(pk.T, qk.T),
+                        stats.entropy(pk, qk, axis=1))
+
+    @array_api_compatible
+    def test_entropy_broadcasting(self, xp):
+        rng = np.random.default_rng(74187315492831452)
+        x = xp.asarray(rng.random(3))
+        y = xp.asarray(rng.random((2, 1)))
+        res = stats.entropy(x, y, axis=-1)
+        xp_assert_equal(res[0], stats.entropy(x, y[0, ...]))
+        xp_assert_equal(res[1], stats.entropy(x, y[1, ...]))
+
+    @array_api_compatible
+    def test_entropy_shape_mismatch(self, xp):
+        x = xp.ones((10, 1, 12))
+        y = xp.ones((11, 2))
+        message = "Array shapes are incompatible for broadcasting."
+        with pytest.raises(ValueError, match=message):
+            stats.entropy(x, y)
+
+    @array_api_compatible
+    def test_input_validation(self, xp):
+        x = xp.ones(10)
+        message = "`base` must be a positive number."
+        with pytest.raises(ValueError, match=message):
+            stats.entropy(x, base=-2)
+
+
+class TestDifferentialEntropy:
+    """
+    Vasicek results are compared with the R package vsgoftest.
+
+    # library(vsgoftest)
+    #
+    # samp <- c(<values>)
+    # entropy.estimate(x = samp, window = <window_length>)
+
+    """
+
+    def test_differential_entropy_vasicek(self):
+
+        random_state = np.random.RandomState(0)
+        values = random_state.standard_normal(100)
+
+        entropy = stats.differential_entropy(values, method='vasicek')
+        assert_allclose(entropy, 1.342551, rtol=1e-6)
+
+        entropy = stats.differential_entropy(values, window_length=1,
+                                             method='vasicek')
+        assert_allclose(entropy, 1.122044, rtol=1e-6)
+
+        entropy = stats.differential_entropy(values, window_length=8,
+                                             method='vasicek')
+        assert_allclose(entropy, 1.349401, rtol=1e-6)
+
+    def test_differential_entropy_vasicek_2d_nondefault_axis(self):
+        random_state = np.random.RandomState(0)
+        values = random_state.standard_normal((3, 100))
+
+        entropy = stats.differential_entropy(values, axis=1, method='vasicek')
+        assert_allclose(
+            entropy,
+            [1.342551, 1.341826, 1.293775],
+            rtol=1e-6,
+        )
+
+        entropy = stats.differential_entropy(values, axis=1, window_length=1,
+                                             method='vasicek')
+        assert_allclose(
+            entropy,
+            [1.122044, 1.102944, 1.129616],
+            rtol=1e-6,
+        )
+
+        entropy = stats.differential_entropy(values, axis=1, window_length=8,
+                                             method='vasicek')
+        assert_allclose(
+            entropy,
+            [1.349401, 1.338514, 1.292332],
+            rtol=1e-6,
+        )
+
+    def test_differential_entropy_raises_value_error(self):
+        random_state = np.random.RandomState(0)
+        values = random_state.standard_normal((3, 100))
+
+        error_str = (
+            r"Window length \({window_length}\) must be positive and less "
+            r"than half the sample size \({sample_size}\)."
+        )
+
+        sample_size = values.shape[1]
+
+        for window_length in {-1, 0, sample_size//2, sample_size}:
+
+            formatted_error_str = error_str.format(
+                window_length=window_length,
+                sample_size=sample_size,
+            )
+
+            with assert_raises(ValueError, match=formatted_error_str):
+                stats.differential_entropy(
+                    values,
+                    window_length=window_length,
+                    axis=1,
+                )
+
+    def test_base_differential_entropy_with_axis_0_is_equal_to_default(self):
+        random_state = np.random.RandomState(0)
+        values = random_state.standard_normal((100, 3))
+
+        entropy = stats.differential_entropy(values, axis=0)
+        default_entropy = stats.differential_entropy(values)
+        assert_allclose(entropy, default_entropy)
+
+    def test_base_differential_entropy_transposed(self):
+        random_state = np.random.RandomState(0)
+        values = random_state.standard_normal((3, 100))
+
+        assert_allclose(
+            stats.differential_entropy(values.T).T,
+            stats.differential_entropy(values, axis=1),
+        )
+
+    def test_input_validation(self):
+        x = np.random.rand(10)
+
+        message = "`base` must be a positive number or `None`."
+        with pytest.raises(ValueError, match=message):
+            stats.differential_entropy(x, base=-2)
+
+        message = "`method` must be one of..."
+        with pytest.raises(ValueError, match=message):
+            stats.differential_entropy(x, method='ekki-ekki')
+
+    @pytest.mark.parametrize('method', ['vasicek', 'van es',
+                                        'ebrahimi', 'correa'])
+    def test_consistency(self, method):
+        # test that method is a consistent estimator
+        n = 10000 if method == 'correa' else 1000000
+        rvs = stats.norm.rvs(size=n, random_state=0)
+        expected = stats.norm.entropy()
+        res = stats.differential_entropy(rvs, method=method)
+        assert_allclose(res, expected, rtol=0.005)
+
+    # values from differential_entropy reference [6], table 1, n=50, m=7
+    norm_rmse_std_cases = {  # method: (RMSE, STD)
+                           'vasicek': (0.198, 0.109),
+                           'van es': (0.212, 0.110),
+                           'correa': (0.135, 0.112),
+                           'ebrahimi': (0.128, 0.109)
+                           }
+
+    @pytest.mark.parametrize('method, expected',
+                             list(norm_rmse_std_cases.items()))
+    def test_norm_rmse_std(self, method, expected):
+        # test that RMSE and standard deviation of estimators matches values
+        # given in differential_entropy reference [6]. Incidentally, also
+        # tests vectorization.
+        reps, n, m = 10000, 50, 7
+        rmse_expected, std_expected = expected
+        rvs = stats.norm.rvs(size=(reps, n), random_state=0)
+        true_entropy = stats.norm.entropy()
+        res = stats.differential_entropy(rvs, window_length=m,
+                                         method=method, axis=-1)
+        assert_allclose(np.sqrt(np.mean((res - true_entropy)**2)),
+                        rmse_expected, atol=0.005)
+        assert_allclose(np.std(res), std_expected, atol=0.002)
+
+    # values from differential_entropy reference [6], table 2, n=50, m=7
+    expon_rmse_std_cases = {  # method: (RMSE, STD)
+                            'vasicek': (0.194, 0.148),
+                            'van es': (0.179, 0.149),
+                            'correa': (0.155, 0.152),
+                            'ebrahimi': (0.151, 0.148)
+                            }
+
+    @pytest.mark.parametrize('method, expected',
+                             list(expon_rmse_std_cases.items()))
+    def test_expon_rmse_std(self, method, expected):
+        # test that RMSE and standard deviation of estimators matches values
+        # given in differential_entropy reference [6]. Incidentally, also
+        # tests vectorization.
+        reps, n, m = 10000, 50, 7
+        rmse_expected, std_expected = expected
+        rvs = stats.expon.rvs(size=(reps, n), random_state=0)
+        true_entropy = stats.expon.entropy()
+        res = stats.differential_entropy(rvs, window_length=m,
+                                         method=method, axis=-1)
+        assert_allclose(np.sqrt(np.mean((res - true_entropy)**2)),
+                        rmse_expected, atol=0.005)
+        assert_allclose(np.std(res), std_expected, atol=0.002)
+
+    @pytest.mark.parametrize('n, method', [(8, 'van es'),
+                                           (12, 'ebrahimi'),
+                                           (1001, 'vasicek')])
+    def test_method_auto(self, n, method):
+        rvs = stats.norm.rvs(size=(n,), random_state=0)
+        res1 = stats.differential_entropy(rvs)
+        res2 = stats.differential_entropy(rvs, method=method)
+        assert res1 == res2

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_fast_gen_inversion.py

@@ -0,0 +1,432 @@
+import pytest
+import warnings
+import numpy as np
+from numpy.testing import (assert_array_equal, assert_allclose,
+                           suppress_warnings)
+from copy import deepcopy
+from scipy.stats.sampling import FastGeneratorInversion
+from scipy import stats
+
+
+def test_bad_args():
+    # loc and scale must be scalar
+    with pytest.raises(ValueError, match="loc must be scalar"):
+        FastGeneratorInversion(stats.norm(loc=(1.2, 1.3)))
+    with pytest.raises(ValueError, match="scale must be scalar"):
+        FastGeneratorInversion(stats.norm(scale=[1.5, 5.7]))
+
+    with pytest.raises(ValueError, match="'test' cannot be used to seed"):
+        FastGeneratorInversion(stats.norm(), random_state="test")
+
+    msg = "Each of the 1 shape parameters must be a scalar"
+    with pytest.raises(ValueError, match=msg):
+        FastGeneratorInversion(stats.gamma([1.3, 2.5]))
+
+    with pytest.raises(ValueError, match="`dist` must be a frozen"):
+        FastGeneratorInversion("xy")
+
+    with pytest.raises(ValueError, match="Distribution 'truncnorm' is not"):
+        FastGeneratorInversion(stats.truncnorm(1.3, 4.5))
+
+
+def test_random_state():
+    # fixed seed
+    gen = FastGeneratorInversion(stats.norm(), random_state=68734509)
+    x1 = gen.rvs(size=10)
+    gen.random_state = 68734509
+    x2 = gen.rvs(size=10)
+    assert_array_equal(x1, x2)
+
+    # Generator
+    urng = np.random.default_rng(20375857)
+    gen = FastGeneratorInversion(stats.norm(), random_state=urng)
+    x1 = gen.rvs(size=10)
+    gen.random_state = np.random.default_rng(20375857)
+    x2 = gen.rvs(size=10)
+    assert_array_equal(x1, x2)
+
+    # RandomState
+    urng = np.random.RandomState(2364)
+    gen = FastGeneratorInversion(stats.norm(), random_state=urng)
+    x1 = gen.rvs(size=10)
+    gen.random_state = np.random.RandomState(2364)
+    x2 = gen.rvs(size=10)
+    assert_array_equal(x1, x2)
+
+    # if evaluate_error is called, it must not interfere with the random_state
+    # used by rvs
+    gen = FastGeneratorInversion(stats.norm(), random_state=68734509)
+    x1 = gen.rvs(size=10)
+    _ = gen.evaluate_error(size=5)  # this will generate 5 uniform rvs
+    x2 = gen.rvs(size=10)
+    gen.random_state = 68734509
+    x3 = gen.rvs(size=20)
+    assert_array_equal(x2, x3[10:])
+
+
+dists_with_params = [
+    ("alpha", (3.5,)),
+    ("anglit", ()),
+    ("argus", (3.5,)),
+    ("argus", (5.1,)),
+    ("beta", (1.5, 0.9)),
+    ("cosine", ()),
+    ("betaprime", (2.5, 3.3)),
+    ("bradford", (1.2,)),
+    ("burr", (1.3, 2.4)),
+    ("burr12", (0.7, 1.2)),
+    ("cauchy", ()),
+    ("chi2", (3.5,)),
+    ("chi", (4.5,)),
+    ("crystalball", (0.7, 1.2)),
+    ("expon", ()),
+    ("gamma", (1.5,)),
+    ("gennorm", (2.7,)),
+    ("gumbel_l", ()),
+    ("gumbel_r", ()),
+    ("hypsecant", ()),
+    ("invgauss", (3.1,)),
+    ("invweibull", (1.5,)),
+    ("laplace", ()),
+    ("logistic", ()),
+    ("maxwell", ()),
+    ("moyal", ()),
+    ("norm", ()),
+    ("pareto", (1.3,)),
+    ("powerlaw", (7.6,)),
+    ("rayleigh", ()),
+    ("semicircular", ()),
+    ("t", (5.7,)),
+    ("wald", ()),
+    ("weibull_max", (2.4,)),
+    ("weibull_min", (1.2,)),
+]
+
+
+@pytest.mark.parametrize(("distname, args"), dists_with_params)
+def test_rvs_and_ppf(distname, args):
+    # check sample against rvs generated by rv_continuous
+    urng = np.random.default_rng(9807324628097097)
+    rng1 = getattr(stats, distname)(*args)
+    rvs1 = rng1.rvs(size=500, random_state=urng)
+    rng2 = FastGeneratorInversion(rng1, random_state=urng)
+    rvs2 = rng2.rvs(size=500)
+    assert stats.cramervonmises_2samp(rvs1, rvs2).pvalue > 0.01
+
+    # check ppf
+    q = [0.001, 0.1, 0.5, 0.9, 0.999]
+    assert_allclose(rng1.ppf(q), rng2.ppf(q), atol=1e-10)
+
+
+@pytest.mark.parametrize(("distname, args"), dists_with_params)
+def test_u_error(distname, args):
+    # check sample against rvs generated by rv_continuous
+    dist = getattr(stats, distname)(*args)
+    with suppress_warnings() as sup:
+        # filter the warnings thrown by UNU.RAN
+        sup.filter(RuntimeWarning)
+        rng = FastGeneratorInversion(dist)
+    u_error, x_error = rng.evaluate_error(
+        size=10_000, random_state=9807324628097097, x_error=False
+    )
+    assert u_error <= 1e-10
+
+
+@pytest.mark.xslow
+@pytest.mark.xfail(reason="geninvgauss CDF is not accurate")
+def test_geninvgauss_uerror():
+    dist = stats.geninvgauss(3.2, 1.5)
+    rng = FastGeneratorInversion(dist)
+    err = rng.evaluate_error(size=10_000, random_state=67982)
+    assert err[0] < 1e-10
+
+
+# TODO: add more distributions
+@pytest.mark.parametrize(("distname, args"), [("beta", (0.11, 0.11))])
+def test_error_extreme_params(distname, args):
+    # take extreme parameters where u-error might not be below the tolerance
+    # due to limitations of floating point arithmetic
+    with suppress_warnings() as sup:
+        # filter the warnings thrown by UNU.RAN for such extreme parameters
+        sup.filter(RuntimeWarning)
+        dist = getattr(stats, distname)(*args)
+        rng = FastGeneratorInversion(dist)
+    u_error, x_error = rng.evaluate_error(
+        size=10_000, random_state=980732462809709732623, x_error=True
+    )
+    if u_error >= 2.5 * 1e-10:
+        assert x_error < 1e-9
+
+
+def test_evaluate_error_inputs():
+    gen = FastGeneratorInversion(stats.norm())
+    with pytest.raises(ValueError, match="size must be an integer"):
+        gen.evaluate_error(size=3.5)
+    with pytest.raises(ValueError, match="size must be an integer"):
+        gen.evaluate_error(size=(3, 3))
+
+
+def test_rvs_ppf_loc_scale():
+    loc, scale = 3.5, 2.3
+    dist = stats.norm(loc=loc, scale=scale)
+    rng = FastGeneratorInversion(dist, random_state=1234)
+    r = rng.rvs(size=1000)
+    r_rescaled = (r - loc) / scale
+    assert stats.cramervonmises(r_rescaled, "norm").pvalue > 0.01
+    q = [0.001, 0.1, 0.5, 0.9, 0.999]
+    assert_allclose(rng._ppf(q), rng.ppf(q), atol=1e-10)
+
+
+def test_domain():
+    # only a basic check that the domain argument is passed to the
+    # UNU.RAN generators
+    rng = FastGeneratorInversion(stats.norm(), domain=(-1, 1))
+    r = rng.rvs(size=100)
+    assert -1 <= r.min() < r.max() <= 1
+
+    # if loc and scale are used, new domain is loc + scale*domain
+    loc, scale = 3.5, 1.3
+    dist = stats.norm(loc=loc, scale=scale)
+    rng = FastGeneratorInversion(dist, domain=(-1.5, 2))
+    r = rng.rvs(size=100)
+    lb, ub = loc - scale * 1.5, loc + scale * 2
+    assert lb <= r.min() < r.max() <= ub
+
+
+@pytest.mark.parametrize(("distname, args, expected"),
+                         [("beta", (3.5, 2.5), (0, 1)),
+                          ("norm", (), (-np.inf, np.inf))])
+def test_support(distname, args, expected):
+    # test that the support is updated if truncation and loc/scale are applied
+    # use beta distribution since it is a transformed betaprime distribution,
+    # so it is important that the correct support is considered
+    # (i.e., the support of beta is (0,1), while betaprime is (0, inf))
+    dist = getattr(stats, distname)(*args)
+    rng = FastGeneratorInversion(dist)
+    assert_array_equal(rng.support(), expected)
+    rng.loc = 1
+    rng.scale = 2
+    assert_array_equal(rng.support(), 1 + 2*np.array(expected))
+
+
+@pytest.mark.parametrize(("distname, args"),
+                         [("beta", (3.5, 2.5)), ("norm", ())])
+def test_support_truncation(distname, args):
+    # similar test for truncation
+    dist = getattr(stats, distname)(*args)
+    rng = FastGeneratorInversion(dist, domain=(0.5, 0.7))
+    assert_array_equal(rng.support(), (0.5, 0.7))
+    rng.loc = 1
+    rng.scale = 2
+    assert_array_equal(rng.support(), (1 + 2 * 0.5, 1 + 2 * 0.7))
+
+
+def test_domain_shift_truncation():
+    # center of norm is zero, it should be shifted to the left endpoint of
+    # domain. if this was not the case, PINV in UNURAN would raise a warning
+    # as the center is not inside the domain
+    with warnings.catch_warnings():
+        warnings.simplefilter("error")
+        rng = FastGeneratorInversion(stats.norm(), domain=(1, 2))
+    r = rng.rvs(size=100)
+    assert 1 <= r.min() < r.max() <= 2
+
+
+def test_non_rvs_methods_with_domain():
+    # as a first step, compare truncated normal against stats.truncnorm
+    rng = FastGeneratorInversion(stats.norm(), domain=(2.3, 3.2))
+    trunc_norm = stats.truncnorm(2.3, 3.2)
+    # take values that are inside and outside the domain
+    x = (2.0, 2.4, 3.0, 3.4)
+    p = (0.01, 0.5, 0.99)
+    assert_allclose(rng._cdf(x), trunc_norm.cdf(x))
+    assert_allclose(rng._ppf(p), trunc_norm.ppf(p))
+    loc, scale = 2, 3
+    rng.loc = 2
+    rng.scale = 3
+    trunc_norm = stats.truncnorm(2.3, 3.2, loc=loc, scale=scale)
+    x = np.array(x) * scale + loc
+    assert_allclose(rng._cdf(x), trunc_norm.cdf(x))
+    assert_allclose(rng._ppf(p), trunc_norm.ppf(p))
+
+    # do another sanity check with beta distribution
+    # in that case, it is important to use the correct domain since beta
+    # is a transformation of betaprime which has a different support
+    rng = FastGeneratorInversion(stats.beta(2.5, 3.5), domain=(0.3, 0.7))
+    rng.loc = 2
+    rng.scale = 2.5
+    # the support is 2.75, , 3.75 (2 + 2.5 * 0.3, 2 + 2.5 * 0.7)
+    assert_array_equal(rng.support(), (2.75, 3.75))
+    x = np.array([2.74, 2.76, 3.74, 3.76])
+    # the cdf needs to be zero outside of the domain
+    y_cdf = rng._cdf(x)
+    assert_array_equal((y_cdf[0], y_cdf[3]), (0, 1))
+    assert np.min(y_cdf[1:3]) > 0
+    # ppf needs to map 0 and 1 to the boundaries
+    assert_allclose(rng._ppf(y_cdf), (2.75, 2.76, 3.74, 3.75))
+
+
+def test_non_rvs_methods_without_domain():
+    norm_dist = stats.norm()
+    rng = FastGeneratorInversion(norm_dist)
+    x = np.linspace(-3, 3, num=10)
+    p = (0.01, 0.5, 0.99)
+    assert_allclose(rng._cdf(x), norm_dist.cdf(x))
+    assert_allclose(rng._ppf(p), norm_dist.ppf(p))
+    loc, scale = 0.5, 1.3
+    rng.loc = loc
+    rng.scale = scale
+    norm_dist = stats.norm(loc=loc, scale=scale)
+    assert_allclose(rng._cdf(x), norm_dist.cdf(x))
+    assert_allclose(rng._ppf(p), norm_dist.ppf(p))
+
+@pytest.mark.parametrize(("domain, x"),
+                         [(None, 0.5),
+                         ((0, 1), 0.5),
+                         ((0, 1), 1.5)])
+def test_scalar_inputs(domain, x):
+    """ pdf, cdf etc should map scalar values to scalars. check with and
+    w/o domain since domain impacts pdf, cdf etc
+    Take x inside and outside of domain """
+    rng = FastGeneratorInversion(stats.norm(), domain=domain)
+    assert np.isscalar(rng._cdf(x))
+    assert np.isscalar(rng._ppf(0.5))
+
+
+def test_domain_argus_large_chi():
+    # for large chi, the Gamma distribution is used and the domain has to be
+    # transformed. this is a test to ensure that the transformation works
+    chi, lb, ub = 5.5, 0.25, 0.75
+    rng = FastGeneratorInversion(stats.argus(chi), domain=(lb, ub))
+    rng.random_state = 4574
+    r = rng.rvs(size=500)
+    assert lb <= r.min() < r.max() <= ub
+    # perform goodness of fit test with conditional cdf
+    cdf = stats.argus(chi).cdf
+    prob = cdf(ub) - cdf(lb)
+    assert stats.cramervonmises(r, lambda x: cdf(x) / prob).pvalue > 0.05
+
+
+def test_setting_loc_scale():
+    rng = FastGeneratorInversion(stats.norm(), random_state=765765864)
+    r1 = rng.rvs(size=1000)
+    rng.loc = 3.0
+    rng.scale = 2.5
+    r2 = rng.rvs(1000)
+    # rescaled r2 should be again standard normal
+    assert stats.cramervonmises_2samp(r1, (r2 - 3) / 2.5).pvalue > 0.05
+    # reset values to default loc=0, scale=1
+    rng.loc = 0
+    rng.scale = 1
+    r2 = rng.rvs(1000)
+    assert stats.cramervonmises_2samp(r1, r2).pvalue > 0.05
+
+
+def test_ignore_shape_range():
+    msg = "No generator is defined for the shape parameters"
+    with pytest.raises(ValueError, match=msg):
+        rng = FastGeneratorInversion(stats.t(0.03))
+    rng = FastGeneratorInversion(stats.t(0.03), ignore_shape_range=True)
+    # we can ignore the recommended range of shape parameters
+    # but u-error can be expected to be too large in that case
+    u_err, _ = rng.evaluate_error(size=1000, random_state=234)
+    assert u_err >= 1e-6
+
+@pytest.mark.xfail_on_32bit(
+    "NumericalInversePolynomial.qrvs fails for Win 32-bit"
+)
+class TestQRVS:
+    def test_input_validation(self):
+        gen = FastGeneratorInversion(stats.norm())
+
+        match = "`qmc_engine` must be an instance of..."
+        with pytest.raises(ValueError, match=match):
+            gen.qrvs(qmc_engine=0)
+
+        match = "`d` must be consistent with dimension of `qmc_engine`."
+        with pytest.raises(ValueError, match=match):
+            gen.qrvs(d=3, qmc_engine=stats.qmc.Halton(2))
+
+    qrngs = [None, stats.qmc.Sobol(1, seed=0), stats.qmc.Halton(3, seed=0)]
+    # `size=None` should not add anything to the shape, `size=1` should
+    sizes = [
+        (None, tuple()),
+        (1, (1,)),
+        (4, (4,)),
+        ((4,), (4,)),
+        ((2, 4), (2, 4)),
+    ]
+    # Neither `d=None` nor `d=1` should add anything to the shape
+    ds = [(None, tuple()), (1, tuple()), (3, (3,))]
+
+    @pytest.mark.parametrize("qrng", qrngs)
+    @pytest.mark.parametrize("size_in, size_out", sizes)
+    @pytest.mark.parametrize("d_in, d_out", ds)
+    def test_QRVS_shape_consistency(self, qrng, size_in, size_out,
+                                    d_in, d_out):
+        gen = FastGeneratorInversion(stats.norm())
+
+        # If d and qrng.d are inconsistent, an error is raised
+        if d_in is not None and qrng is not None and qrng.d != d_in:
+            match = "`d` must be consistent with dimension of `qmc_engine`."
+            with pytest.raises(ValueError, match=match):
+                gen.qrvs(size_in, d=d_in, qmc_engine=qrng)
+            return
+
+        # Sometimes d is really determined by qrng
+        if d_in is None and qrng is not None and qrng.d != 1:
+            d_out = (qrng.d,)
+
+        shape_expected = size_out + d_out
+
+        qrng2 = deepcopy(qrng)
+        qrvs = gen.qrvs(size=size_in, d=d_in, qmc_engine=qrng)
+        if size_in is not None:
+            assert qrvs.shape == shape_expected
+
+        if qrng2 is not None:
+            uniform = qrng2.random(np.prod(size_in) or 1)
+            qrvs2 = stats.norm.ppf(uniform).reshape(shape_expected)
+            assert_allclose(qrvs, qrvs2, atol=1e-12)
+
+    def test_QRVS_size_tuple(self):
+        # QMCEngine samples are always of shape (n, d). When `size` is a tuple,
+        # we set `n = prod(size)` in the call to qmc_engine.random, transform
+        # the sample, and reshape it to the final dimensions. When we reshape,
+        # we need to be careful, because the _columns_ of the sample returned
+        # by a QMCEngine are "independent"-ish, but the elements within the
+        # columns are not. We need to make sure that this doesn't get mixed up
+        # by reshaping: qrvs[..., i] should remain "independent"-ish of
+        # qrvs[..., i+1], but the elements within qrvs[..., i] should be
+        # transformed from the same low-discrepancy sequence.
+
+        gen = FastGeneratorInversion(stats.norm())
+
+        size = (3, 4)
+        d = 5
+        qrng = stats.qmc.Halton(d, seed=0)
+        qrng2 = stats.qmc.Halton(d, seed=0)
+
+        uniform = qrng2.random(np.prod(size))
+
+        qrvs = gen.qrvs(size=size, d=d, qmc_engine=qrng)
+        qrvs2 = stats.norm.ppf(uniform)
+
+        for i in range(d):
+            sample = qrvs[..., i]
+            sample2 = qrvs2[:, i].reshape(size)
+            assert_allclose(sample, sample2, atol=1e-12)
+
+
+def test_burr_overflow():
+    # this case leads to an overflow error if math.exp is used
+    # in the definition of the burr pdf instead of np.exp
+    # a direct implementation of the PDF as x**(-c-1) / (1+x**(-c))**(d+1)
+    # also leads to an overflow error in the setup
+    args = (1.89128135, 0.30195177)
+    with suppress_warnings() as sup:
+        # filter potential overflow warning
+        sup.filter(RuntimeWarning)
+        gen = FastGeneratorInversion(stats.burr(*args))
+    u_error, _ = gen.evaluate_error(random_state=4326)
+    assert u_error <= 1e-10

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_fit.py

@@ -0,0 +1,1038 @@
+import os
+import numpy as np
+import numpy.testing as npt
+from numpy.testing import assert_allclose, assert_equal
+import pytest
+from scipy import stats
+from scipy.optimize import differential_evolution
+
+from .test_continuous_basic import distcont
+from scipy.stats._distn_infrastructure import FitError
+from scipy.stats._distr_params import distdiscrete
+from scipy.stats import goodness_of_fit
+
+
+# this is not a proper statistical test for convergence, but only
+# verifies that the estimate and true values don't differ by too much
+
+fit_sizes = [1000, 5000, 10000]  # sample sizes to try
+
+thresh_percent = 0.25  # percent of true parameters for fail cut-off
+thresh_min = 0.75  # minimum difference estimate - true to fail test
+
+mle_failing_fits = [
+        'gausshyper',
+        'genexpon',
+        'gengamma',
+        'irwinhall',
+        'kappa4',
+        'ksone',
+        'kstwo',
+        'ncf',
+        'ncx2',
+        'truncexpon',
+        'tukeylambda',
+        'vonmises',
+        'levy_stable',
+        'trapezoid',
+        'truncweibull_min',
+        'studentized_range',
+]
+
+# these pass but are XSLOW (>1s)
+mle_Xslow_fits = ['betaprime', 'crystalball', 'exponweib', 'f', 'geninvgauss',
+                  'jf_skew_t', 'recipinvgauss', 'rel_breitwigner', 'vonmises_line']
+
+# The MLE fit method of these distributions doesn't perform well when all
+# parameters are fit, so test them with the location fixed at 0.
+mle_use_floc0 = [
+    'burr',
+    'chi',
+    'chi2',
+    'mielke',
+    'pearson3',
+    'genhalflogistic',
+    'rdist',
+    'pareto',
+    'powerlaw',  # distfn.nnlf(est2, rvs) > distfn.nnlf(est1, rvs) otherwise
+    'powerlognorm',
+    'wrapcauchy',
+    'rel_breitwigner',
+]
+
+mm_failing_fits = ['alpha', 'betaprime', 'burr', 'burr12', 'cauchy', 'chi',
+                   'chi2', 'crystalball', 'dgamma', 'dweibull', 'f',
+                   'fatiguelife', 'fisk', 'foldcauchy', 'genextreme',
+                   'gengamma', 'genhyperbolic', 'gennorm', 'genpareto',
+                   'halfcauchy', 'invgamma', 'invweibull', 'irwinhall', 'jf_skew_t',
+                   'johnsonsu', 'kappa3', 'ksone', 'kstwo', 'levy', 'levy_l',
+                   'levy_stable', 'loglaplace', 'lomax', 'mielke', 'nakagami',
+                   'ncf', 'nct', 'ncx2', 'pareto', 'powerlognorm', 'powernorm',
+                   'rel_breitwigner', 'skewcauchy', 't', 'trapezoid', 'triang',
+                   'truncpareto', 'truncweibull_min', 'tukeylambda',
+                   'studentized_range']
+
+# not sure if these fail, but they caused my patience to fail
+mm_XXslow_fits = ['argus', 'exponpow', 'exponweib', 'gausshyper', 'genexpon',
+                  'genhalflogistic', 'halfgennorm', 'gompertz', 'johnsonsb',
+                  'kappa4', 'kstwobign', 'recipinvgauss',
+                  'truncexpon', 'vonmises', 'vonmises_line']
+
+# these pass but are XSLOW (>1s)
+mm_Xslow_fits = ['wrapcauchy']
+
+failing_fits = {"MM": mm_failing_fits + mm_XXslow_fits, "MLE": mle_failing_fits}
+xslow_fits = {"MM": mm_Xslow_fits, "MLE": mle_Xslow_fits}
+fail_interval_censored = {"truncpareto"}
+
+# Don't run the fit test on these:
+skip_fit = [
+    'erlang',  # Subclass of gamma, generates a warning.
+    'genhyperbolic', 'norminvgauss',  # too slow
+]
+
+
+def cases_test_cont_fit():
+    # this tests the closeness of the estimated parameters to the true
+    # parameters with fit method of continuous distributions
+    # Note: is slow, some distributions don't converge with sample
+    # size <= 10000
+    for distname, arg in distcont:
+        if distname not in skip_fit:
+            yield distname, arg
+
+
+@pytest.mark.slow
+@pytest.mark.parametrize('distname,arg', cases_test_cont_fit())
+@pytest.mark.parametrize('method', ["MLE", "MM"])
+def test_cont_fit(distname, arg, method):
+    run_xfail = int(os.getenv('SCIPY_XFAIL', default=False))
+    run_xslow = int(os.getenv('SCIPY_XSLOW', default=False))
+
+    if distname in failing_fits[method] and not run_xfail:
+        # The generic `fit` method can't be expected to work perfectly for all
+        # distributions, data, and guesses. Some failures are expected.
+        msg = "Failure expected; set environment variable SCIPY_XFAIL=1 to run."
+        pytest.xfail(msg)
+
+    if distname in xslow_fits[method] and not run_xslow:
+        msg = "Very slow; set environment variable SCIPY_XSLOW=1 to run."
+        pytest.skip(msg)
+
+    distfn = getattr(stats, distname)
+
+    truearg = np.hstack([arg, [0.0, 1.0]])
+    diffthreshold = np.max(np.vstack([truearg*thresh_percent,
+                                      np.full(distfn.numargs+2, thresh_min)]),
+                           0)
+
+    for fit_size in fit_sizes:
+        # Note that if a fit succeeds, the other fit_sizes are skipped
+        np.random.seed(1234)
+
+        with np.errstate(all='ignore'):
+            rvs = distfn.rvs(size=fit_size, *arg)
+            if method == 'MLE' and distfn.name in mle_use_floc0:
+                kwds = {'floc': 0}
+            else:
+                kwds = {}
+            # start with default values
+            est = distfn.fit(rvs, method=method, **kwds)
+            if method == 'MLE':
+                # Trivial test of the use of CensoredData.  The fit() method
+                # will check that data contains no actual censored data, and
+                # do a regular uncensored fit.
+                data1 = stats.CensoredData(rvs)
+                est1 = distfn.fit(data1, **kwds)
+                msg = ('Different results fitting uncensored data wrapped as'
+                       f' CensoredData: {distfn.name}: est={est} est1={est1}')
+                assert_allclose(est1, est, rtol=1e-10, err_msg=msg)
+            if method == 'MLE' and distname not in fail_interval_censored:
+                # Convert the first `nic` values in rvs to interval-censored
+                # values. The interval is small, so est2 should be close to
+                # est.
+                nic = 15
+                interval = np.column_stack((rvs, rvs))
+                interval[:nic, 0] *= 0.99
+                interval[:nic, 1] *= 1.01
+                interval.sort(axis=1)
+                data2 = stats.CensoredData(interval=interval)
+                est2 = distfn.fit(data2, **kwds)
+                msg = ('Different results fitting interval-censored'
+                       f' data: {distfn.name}: est={est} est2={est2}')
+                assert_allclose(est2, est, rtol=0.05, err_msg=msg)
+
+        diff = est - truearg
+
+        # threshold for location
+        diffthreshold[-2] = np.max([np.abs(rvs.mean())*thresh_percent,
+                                    thresh_min])
+
+        if np.any(np.isnan(est)):
+            raise AssertionError('nan returned in fit')
+        else:
+            if np.all(np.abs(diff) <= diffthreshold):
+                break
+    else:
+        txt = 'parameter: %s\n' % str(truearg)
+        txt += 'estimated: %s\n' % str(est)
+        txt += 'diff     : %s\n' % str(diff)
+        raise AssertionError('fit not very good in %s\n' % distfn.name + txt)
+
+
+def _check_loc_scale_mle_fit(name, data, desired, atol=None):
+    d = getattr(stats, name)
+    actual = d.fit(data)[-2:]
+    assert_allclose(actual, desired, atol=atol,
+                    err_msg='poor mle fit of (loc, scale) in %s' % name)
+
+
+def test_non_default_loc_scale_mle_fit():
+    data = np.array([1.01, 1.78, 1.78, 1.78, 1.88, 1.88, 1.88, 2.00])
+    _check_loc_scale_mle_fit('uniform', data, [1.01, 0.99], 1e-3)
+    _check_loc_scale_mle_fit('expon', data, [1.01, 0.73875], 1e-3)
+
+
+def test_expon_fit():
+    """gh-6167"""
+    data = [0, 0, 0, 0, 2, 2, 2, 2]
+    phat = stats.expon.fit(data, floc=0)
+    assert_allclose(phat, [0, 1.0], atol=1e-3)
+
+
+def test_fit_error():
+    data = np.concatenate([np.zeros(29), np.ones(21)])
+    message = "Optimization converged to parameters that are..."
+    with pytest.raises(FitError, match=message), \
+            pytest.warns(RuntimeWarning):
+        stats.beta.fit(data)
+
+
+@pytest.mark.parametrize("dist, params",
+                         [(stats.norm, (0.5, 2.5)),  # type: ignore[attr-defined]
+                          (stats.binom, (10, 0.3, 2))])  # type: ignore[attr-defined]
+def test_nnlf_and_related_methods(dist, params):
+    rng = np.random.default_rng(983459824)
+
+    if hasattr(dist, 'pdf'):
+        logpxf = dist.logpdf
+    else:
+        logpxf = dist.logpmf
+
+    x = dist.rvs(*params, size=100, random_state=rng)
+    ref = -logpxf(x, *params).sum()
+    res1 = dist.nnlf(params, x)
+    res2 = dist._penalized_nnlf(params, x)
+    assert_allclose(res1, ref)
+    assert_allclose(res2, ref)
+
+
+def cases_test_fit_mle():
+    # These fail default test or hang
+    skip_basic_fit = {'argus', 'irwinhall', 'foldnorm', 'truncpareto',
+                      'truncweibull_min', 'ksone', 'levy_stable',
+                      'studentized_range', 'kstwo', 'arcsine'}
+
+    # Please keep this list in alphabetical order...
+    slow_basic_fit = {'alpha', 'betaprime', 'binom', 'bradford', 'burr12',
+                      'chi', 'crystalball', 'dweibull', 'erlang', 'exponnorm',
+                      'exponpow', 'f', 'fatiguelife', 'fisk', 'foldcauchy', 'gamma',
+                      'genexpon', 'genextreme', 'gennorm', 'genpareto',
+                      'gompertz', 'halfgennorm', 'invgamma', 'invgauss', 'invweibull',
+                      'jf_skew_t', 'johnsonsb', 'johnsonsu', 'kappa3',
+                      'kstwobign', 'loglaplace', 'lognorm', 'lomax', 'mielke',
+                      'nakagami', 'nbinom', 'norminvgauss',
+                      'pareto', 'pearson3', 'powerlaw', 'powernorm',
+                      'randint', 'rdist', 'recipinvgauss', 'rice', 'skewnorm',
+                      't', 'uniform', 'weibull_max', 'weibull_min', 'wrapcauchy'}
+
+    # Please keep this list in alphabetical order...
+    xslow_basic_fit = {'beta', 'betabinom', 'betanbinom', 'burr', 'exponweib',
+                       'gausshyper', 'gengamma', 'genhalflogistic',
+                       'genhyperbolic', 'geninvgauss',
+                       'hypergeom', 'kappa4', 'loguniform',
+                       'ncf', 'nchypergeom_fisher', 'nchypergeom_wallenius',
+                       'nct', 'ncx2', 'nhypergeom',
+                       'powerlognorm', 'reciprocal', 'rel_breitwigner',
+                       'skellam', 'trapezoid', 'triang', 'truncnorm',
+                       'tukeylambda', 'vonmises', 'zipfian'}
+
+    for dist in dict(distdiscrete + distcont):
+        if dist in skip_basic_fit or not isinstance(dist, str):
+            reason = "tested separately"
+            yield pytest.param(dist, marks=pytest.mark.skip(reason=reason))
+        elif dist in slow_basic_fit:
+            reason = "too slow (>= 0.25s)"
+            yield pytest.param(dist, marks=pytest.mark.slow(reason=reason))
+        elif dist in xslow_basic_fit:
+            reason = "too slow (>= 1.0s)"
+            yield pytest.param(dist, marks=pytest.mark.xslow(reason=reason))
+        else:
+            yield dist
+
+
+def cases_test_fit_mse():
+    # the first four are so slow that I'm not sure whether they would pass
+    skip_basic_fit = {'levy_stable', 'studentized_range', 'ksone', 'skewnorm',
+                      'irwinhall', # hangs
+                      'norminvgauss',  # super slow (~1 hr) but passes
+                      'kstwo',  # very slow (~25 min) but passes
+                      'geninvgauss',  # quite slow (~4 minutes) but passes
+                      'gausshyper', 'genhyperbolic',  # integration warnings
+                      'tukeylambda',  # close, but doesn't meet tolerance
+                      'vonmises',  # can have negative CDF; doesn't play nice
+                      'argus'}  # doesn't meet tolerance; tested separately
+
+    # Please keep this list in alphabetical order...
+    slow_basic_fit = {'alpha', 'anglit', 'arcsine', 'betabinom', 'bradford',
+                      'chi', 'chi2', 'crystalball', 'dweibull',
+                      'erlang', 'exponnorm', 'exponpow', 'exponweib',
+                      'fatiguelife', 'fisk', 'foldcauchy', 'foldnorm',
+                      'gamma', 'genexpon', 'genextreme', 'genhalflogistic',
+                      'genlogistic', 'genpareto', 'gompertz',
+                      'hypergeom', 'invweibull',
+                      'johnsonsu', 'kappa3', 'kstwobign',
+                      'laplace_asymmetric', 'loggamma', 'loglaplace',
+                      'lognorm', 'lomax',
+                      'maxwell', 'nhypergeom',
+                      'pareto', 'powernorm', 'randint', 'recipinvgauss',
+                      'semicircular',
+                      't', 'triang', 'truncexpon', 'truncpareto',
+                      'uniform',
+                      'wald', 'weibull_max', 'weibull_min', 'wrapcauchy'}
+
+    # Please keep this list in alphabetical order...
+    xslow_basic_fit = {'argus', 'beta', 'betaprime', 'burr', 'burr12',
+                       'dgamma', 'f', 'gengamma', 'gennorm',
+                       'halfgennorm', 'invgamma', 'invgauss', 'jf_skew_t',
+                       'johnsonsb', 'kappa4', 'loguniform', 'mielke',
+                       'nakagami', 'ncf', 'nchypergeom_fisher',
+                       'nchypergeom_wallenius', 'nct', 'ncx2',
+                       'pearson3', 'powerlaw', 'powerlognorm',
+                       'rdist', 'reciprocal', 'rel_breitwigner', 'rice',
+                       'trapezoid', 'truncnorm', 'truncweibull_min',
+                       'vonmises_line', 'zipfian'}
+
+    warns_basic_fit = {'skellam'}  # can remove mark after gh-14901 is resolved
+
+    for dist in dict(distdiscrete + distcont):
+        if dist in skip_basic_fit or not isinstance(dist, str):
+            reason = "Fails. Oh well."
+            yield pytest.param(dist, marks=pytest.mark.skip(reason=reason))
+        elif dist in slow_basic_fit:
+            reason = "too slow (>= 0.25s)"
+            yield pytest.param(dist, marks=pytest.mark.slow(reason=reason))
+        elif dist in xslow_basic_fit:
+            reason = "too slow (>= 1.0s)"
+            yield pytest.param(dist, marks=pytest.mark.xslow(reason=reason))
+        elif dist in warns_basic_fit:
+            mark = pytest.mark.filterwarnings('ignore::RuntimeWarning')
+            yield pytest.param(dist, marks=mark)
+        else:
+            yield dist
+
+
+def cases_test_fitstart():
+    for distname, shapes in dict(distcont).items():
+        if (not isinstance(distname, str) or
+                distname in {'studentized_range', 'recipinvgauss'}):  # slow
+            continue
+        yield distname, shapes
+
+
+@pytest.mark.parametrize('distname, shapes', cases_test_fitstart())
+def test_fitstart(distname, shapes):
+    dist = getattr(stats, distname)
+    rng = np.random.default_rng(216342614)
+    data = rng.random(10)
+
+    with np.errstate(invalid='ignore', divide='ignore'):  # irrelevant to test
+        guess = dist._fitstart(data)
+
+    assert dist._argcheck(*guess[:-2])
+
+
+def assert_nlff_less_or_close(dist, data, params1, params0, rtol=1e-7, atol=0,
+                              nlff_name='nnlf'):
+    nlff = getattr(dist, nlff_name)
+    nlff1 = nlff(params1, data)
+    nlff0 = nlff(params0, data)
+    if not (nlff1 < nlff0):
+        np.testing.assert_allclose(nlff1, nlff0, rtol=rtol, atol=atol)
+
+
+class TestFit:
+    dist = stats.binom  # type: ignore[attr-defined]
+    seed = 654634816187
+    rng = np.random.default_rng(seed)
+    data = stats.binom.rvs(5, 0.5, size=100, random_state=rng)  # type: ignore[attr-defined]  # noqa: E501
+    shape_bounds_a = [(1, 10), (0, 1)]
+    shape_bounds_d = {'n': (1, 10), 'p': (0, 1)}
+    atol = 5e-2
+    rtol = 1e-2
+    tols = {'atol': atol, 'rtol': rtol}
+
+    def opt(self, *args, **kwds):
+        return differential_evolution(*args, seed=0, **kwds)
+
+    def test_dist_iv(self):
+        message = "`dist` must be an instance of..."
+        with pytest.raises(ValueError, match=message):
+            stats.fit(10, self.data, self.shape_bounds_a)
+
+    def test_data_iv(self):
+        message = "`data` must be exactly one-dimensional."
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, [[1, 2, 3]], self.shape_bounds_a)
+
+        message = "All elements of `data` must be finite numbers."
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, [1, 2, 3, np.nan], self.shape_bounds_a)
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, [1, 2, 3, np.inf], self.shape_bounds_a)
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, ['1', '2', '3'], self.shape_bounds_a)
+
+    def test_bounds_iv(self):
+        message = "Bounds provided for the following unrecognized..."
+        shape_bounds = {'n': (1, 10), 'p': (0, 1), '1': (0, 10)}
+        with pytest.warns(RuntimeWarning, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+        message = "Each element of a `bounds` sequence must be a tuple..."
+        shape_bounds = [(1, 10, 3), (0, 1)]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+        message = "Each element of `bounds` must be a tuple specifying..."
+        shape_bounds = [(1, 10, 3), (0, 1, 0.5)]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+        shape_bounds = [1, 0]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+        message = "A `bounds` sequence must contain at least 2 elements..."
+        shape_bounds = [(1, 10)]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+        message = "A `bounds` sequence may not contain more than 3 elements..."
+        bounds = [(1, 10), (1, 10), (1, 10), (1, 10)]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, bounds)
+
+        message = "There are no values for `p` on the interval..."
+        shape_bounds = {'n': (1, 10), 'p': (1, 0)}
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+        message = "There are no values for `n` on the interval..."
+        shape_bounds = [(10, 1), (0, 1)]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+        message = "There are no integer values for `n` on the interval..."
+        shape_bounds = [(1.4, 1.6), (0, 1)]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+        message = "The intersection of user-provided bounds for `n`"
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data)
+        shape_bounds = [(-np.inf, np.inf), (0, 1)]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, shape_bounds)
+
+    def test_guess_iv(self):
+        message = "Guesses provided for the following unrecognized..."
+        guess = {'n': 1, 'p': 0.5, '1': 255}
+        with pytest.warns(RuntimeWarning, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+        message = "Each element of `guess` must be a scalar..."
+        guess = {'n': 1, 'p': 'hi'}
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+        guess = [1, 'f']
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+        guess = [[1, 2]]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+        message = "A `guess` sequence must contain at least 2..."
+        guess = [1]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+        message = "A `guess` sequence may not contain more than 3..."
+        guess = [1, 2, 3, 4]
+        with pytest.raises(ValueError, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+        message = "Guess for parameter `n` rounded.*|Guess for parameter `p` clipped.*"
+        guess = {'n': 4.5, 'p': -0.5}
+        with pytest.warns(RuntimeWarning, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+        message = "Guess for parameter `loc` rounded..."
+        guess = [5, 0.5, 0.5]
+        with pytest.warns(RuntimeWarning, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+        message = "Guess for parameter `p` clipped..."
+        guess = {'n': 5, 'p': -0.5}
+        with pytest.warns(RuntimeWarning, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+        message = "Guess for parameter `loc` clipped..."
+        guess = [5, 0.5, 1]
+        with pytest.warns(RuntimeWarning, match=message):
+            stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
+
+    def basic_fit_test(self, dist_name, method):
+
+        N = 5000
+        dist_data = dict(distcont + distdiscrete)
+        rng = np.random.default_rng(self.seed)
+        dist = getattr(stats, dist_name)
+        shapes = np.array(dist_data[dist_name])
+        bounds = np.empty((len(shapes) + 2, 2), dtype=np.float64)
+        bounds[:-2, 0] = shapes/10.**np.sign(shapes)
+        bounds[:-2, 1] = shapes*10.**np.sign(shapes)
+        bounds[-2] = (0, 10)
+        bounds[-1] = (1e-16, 10)
+        loc = rng.uniform(*bounds[-2])
+        scale = rng.uniform(*bounds[-1])
+        ref = list(dist_data[dist_name]) + [loc, scale]
+
+        if getattr(dist, 'pmf', False):
+            ref = ref[:-1]
+            ref[-1] = np.floor(loc)
+            data = dist.rvs(*ref, size=N, random_state=rng)
+            bounds = bounds[:-1]
+        if getattr(dist, 'pdf', False):
+            data = dist.rvs(*ref, size=N, random_state=rng)
+
+        with npt.suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, "overflow encountered")
+            res = stats.fit(dist, data, bounds, method=method,
+                            optimizer=self.opt)
+
+        nlff_names = {'mle': 'nnlf', 'mse': '_penalized_nlpsf'}
+        nlff_name = nlff_names[method]
+        assert_nlff_less_or_close(dist, data, res.params, ref, **self.tols,
+                                  nlff_name=nlff_name)
+
+    @pytest.mark.parametrize("dist_name", cases_test_fit_mle())
+    def test_basic_fit_mle(self, dist_name):
+        self.basic_fit_test(dist_name, "mle")
+
+    @pytest.mark.parametrize("dist_name", cases_test_fit_mse())
+    def test_basic_fit_mse(self, dist_name):
+        self.basic_fit_test(dist_name, "mse")
+
+    def test_arcsine(self):
+        # Can't guarantee that all distributions will fit all data with
+        # arbitrary bounds. This distribution just happens to fail above.
+        # Try something slightly different.
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+        dist = stats.arcsine
+        shapes = (1., 2.)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+        shape_bounds = {'loc': (0.1, 10), 'scale': (0.1, 10)}
+        res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
+        assert_nlff_less_or_close(dist, data, res.params, shapes, **self.tols)
+
+    @pytest.mark.parametrize("method", ('mle', 'mse'))
+    def test_argus(self, method):
+        # Can't guarantee that all distributions will fit all data with
+        # arbitrary bounds. This distribution just happens to fail above.
+        # Try something slightly different.
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+        dist = stats.argus
+        shapes = (1., 2., 3.)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+        shape_bounds = {'chi': (0.1, 10), 'loc': (0.1, 10), 'scale': (0.1, 10)}
+        res = stats.fit(dist, data, shape_bounds, optimizer=self.opt, method=method)
+
+        assert_nlff_less_or_close(dist, data, res.params, shapes, **self.tols)
+
+    def test_foldnorm(self):
+        # Can't guarantee that all distributions will fit all data with
+        # arbitrary bounds. This distribution just happens to fail above.
+        # Try something slightly different.
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+        dist = stats.foldnorm
+        shapes = (1.952125337355587, 2., 3.)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+        shape_bounds = {'c': (0.1, 10), 'loc': (0.1, 10), 'scale': (0.1, 10)}
+        res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
+
+        assert_nlff_less_or_close(dist, data, res.params, shapes, **self.tols)
+
+    def test_truncpareto(self):
+        # Can't guarantee that all distributions will fit all data with
+        # arbitrary bounds. This distribution just happens to fail above.
+        # Try something slightly different.
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+        dist = stats.truncpareto
+        shapes = (1.8, 5.3, 2.3, 4.1)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+        shape_bounds = [(0.1, 10)]*4
+        res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
+
+        assert_nlff_less_or_close(dist, data, res.params, shapes, **self.tols)
+
+    def test_truncweibull_min(self):
+        # Can't guarantee that all distributions will fit all data with
+        # arbitrary bounds. This distribution just happens to fail above.
+        # Try something slightly different.
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+        dist = stats.truncweibull_min
+        shapes = (2.5, 0.25, 1.75, 2., 3.)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+        shape_bounds = [(0.1, 10)]*5
+        res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
+
+        assert_nlff_less_or_close(dist, data, res.params, shapes, **self.tols)
+
+    def test_missing_shape_bounds(self):
+        # some distributions have a small domain w.r.t. a parameter, e.g.
+        # $p \in [0, 1]$ for binomial distribution
+        # User does not need to provide these because the intersection of the
+        # user's bounds (none) and the distribution's domain is finite
+        N = 1000
+        rng = np.random.default_rng(self.seed)
+
+        dist = stats.binom
+        n, p, loc = 10, 0.65, 0
+        data = dist.rvs(n, p, loc=loc, size=N, random_state=rng)
+        shape_bounds = {'n': np.array([0, 20])}  # check arrays are OK, too
+        res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
+        assert_allclose(res.params, (n, p, loc), **self.tols)
+
+        dist = stats.bernoulli
+        p, loc = 0.314159, 0
+        data = dist.rvs(p, loc=loc, size=N, random_state=rng)
+        res = stats.fit(dist, data, optimizer=self.opt)
+        assert_allclose(res.params, (p, loc), **self.tols)
+
+    def test_fit_only_loc_scale(self):
+        # fit only loc
+        N = 5000
+        rng = np.random.default_rng(self.seed)
+
+        dist = stats.norm
+        loc, scale = 1.5, 1
+        data = dist.rvs(loc=loc, size=N, random_state=rng)
+        loc_bounds = (0, 5)
+        bounds = {'loc': loc_bounds}
+        res = stats.fit(dist, data, bounds, optimizer=self.opt)
+        assert_allclose(res.params, (loc, scale), **self.tols)
+
+        # fit only scale
+        loc, scale = 0, 2.5
+        data = dist.rvs(scale=scale, size=N, random_state=rng)
+        scale_bounds = (0.01, 5)
+        bounds = {'scale': scale_bounds}
+        res = stats.fit(dist, data, bounds, optimizer=self.opt)
+        assert_allclose(res.params, (loc, scale), **self.tols)
+
+        # fit only loc and scale
+        dist = stats.norm
+        loc, scale = 1.5, 2.5
+        data = dist.rvs(loc=loc, scale=scale, size=N, random_state=rng)
+        bounds = {'loc': loc_bounds, 'scale': scale_bounds}
+        res = stats.fit(dist, data, bounds, optimizer=self.opt)
+        assert_allclose(res.params, (loc, scale), **self.tols)
+
+    def test_everything_fixed(self):
+        N = 5000
+        rng = np.random.default_rng(self.seed)
+
+        dist = stats.norm
+        loc, scale = 1.5, 2.5
+        data = dist.rvs(loc=loc, scale=scale, size=N, random_state=rng)
+
+        # loc, scale fixed to 0, 1 by default
+        res = stats.fit(dist, data)
+        assert_allclose(res.params, (0, 1), **self.tols)
+
+        # loc, scale explicitly fixed
+        bounds = {'loc': (loc, loc), 'scale': (scale, scale)}
+        res = stats.fit(dist, data, bounds)
+        assert_allclose(res.params, (loc, scale), **self.tols)
+
+        # `n` gets fixed during polishing
+        dist = stats.binom
+        n, p, loc = 10, 0.65, 0
+        data = dist.rvs(n, p, loc=loc, size=N, random_state=rng)
+        shape_bounds = {'n': (0, 20), 'p': (0.65, 0.65)}
+        res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
+        assert_allclose(res.params, (n, p, loc), **self.tols)
+
+    def test_failure(self):
+        N = 5000
+        rng = np.random.default_rng(self.seed)
+
+        dist = stats.nbinom
+        shapes = (5, 0.5)
+        data = dist.rvs(*shapes, size=N, random_state=rng)
+
+        assert data.min() == 0
+        # With lower bounds on location at 0.5, likelihood is zero
+        bounds = [(0, 30), (0, 1), (0.5, 10)]
+        res = stats.fit(dist, data, bounds)
+        message = "Optimization converged to parameter values that are"
+        assert res.message.startswith(message)
+        assert res.success is False
+
+    @pytest.mark.xslow
+    def test_guess(self):
+        # Test that guess helps DE find the desired solution
+        N = 2000
+        # With some seeds, `fit` doesn't need a guess
+        rng = np.random.default_rng(196390444561)
+        dist = stats.nhypergeom
+        params = (20, 7, 12, 0)
+        bounds = [(2, 200), (0.7, 70), (1.2, 120), (0, 10)]
+
+        data = dist.rvs(*params, size=N, random_state=rng)
+
+        res = stats.fit(dist, data, bounds, optimizer=self.opt)
+        assert not np.allclose(res.params, params, **self.tols)
+
+        res = stats.fit(dist, data, bounds, guess=params, optimizer=self.opt)
+        assert_allclose(res.params, params, **self.tols)
+
+    def test_mse_accuracy_1(self):
+        # Test maximum spacing estimation against example from Wikipedia
+        # https://en.wikipedia.org/wiki/Maximum_spacing_estimation#Examples
+        data = [2, 4]
+        dist = stats.expon
+        bounds = {'loc': (0, 0), 'scale': (1e-8, 10)}
+        res_mle = stats.fit(dist, data, bounds=bounds, method='mle')
+        assert_allclose(res_mle.params.scale, 3, atol=1e-3)
+        res_mse = stats.fit(dist, data, bounds=bounds, method='mse')
+        assert_allclose(res_mse.params.scale, 3.915, atol=1e-3)
+
+    def test_mse_accuracy_2(self):
+        # Test maximum spacing estimation against example from Wikipedia
+        # https://en.wikipedia.org/wiki/Maximum_spacing_estimation#Examples
+        rng = np.random.default_rng(9843212616816518964)
+
+        dist = stats.uniform
+        n = 10
+        data = dist(3, 6).rvs(size=n, random_state=rng)
+        bounds = {'loc': (0, 10), 'scale': (1e-8, 10)}
+        res = stats.fit(dist, data, bounds=bounds, method='mse')
+        # (loc=3.608118420015416, scale=5.509323262055043)
+
+        x = np.sort(data)
+        a = (n*x[0] - x[-1])/(n - 1)
+        b = (n*x[-1] - x[0])/(n - 1)
+        ref = a, b-a  # (3.6081133632151503, 5.509328130317254)
+        assert_allclose(res.params, ref, rtol=1e-4)
+
+
+# Data from Matlab: https://www.mathworks.com/help/stats/lillietest.html
+examgrades = [65, 61, 81, 88, 69, 89, 55, 84, 86, 84, 71, 81, 84, 81, 78, 67,
+              96, 66, 73, 75, 59, 71, 69, 63, 79, 76, 63, 85, 87, 88, 80, 71,
+              65, 84, 71, 75, 81, 79, 64, 65, 84, 77, 70, 75, 84, 75, 73, 92,
+              90, 79, 80, 71, 73, 71, 58, 79, 73, 64, 77, 82, 81, 59, 54, 82,
+              57, 79, 79, 73, 74, 82, 63, 64, 73, 69, 87, 68, 81, 73, 83, 73,
+              80, 73, 73, 71, 66, 78, 64, 74, 68, 67, 75, 75, 80, 85, 74, 76,
+              80, 77, 93, 70, 86, 80, 81, 83, 68, 60, 85, 64, 74, 82, 81, 77,
+              66, 85, 75, 81, 69, 60, 83, 72]
+
+
+class TestGoodnessOfFit:
+
+    def test_gof_iv(self):
+        dist = stats.norm
+        x = [1, 2, 3]
+
+        message = r"`dist` must be a \(non-frozen\) instance of..."
+        with pytest.raises(TypeError, match=message):
+            goodness_of_fit(stats.norm(), x)
+
+        message = "`data` must be a one-dimensional array of numbers."
+        with pytest.raises(ValueError, match=message):
+            goodness_of_fit(dist, [[1, 2, 3]])
+
+        message = "`statistic` must be one of..."
+        with pytest.raises(ValueError, match=message):
+            goodness_of_fit(dist, x, statistic='mm')
+
+        message = "`n_mc_samples` must be an integer."
+        with pytest.raises(TypeError, match=message):
+            goodness_of_fit(dist, x, n_mc_samples=1000.5)
+
+        message = "'herring' cannot be used to seed a"
+        with pytest.raises(ValueError, match=message):
+            goodness_of_fit(dist, x, random_state='herring')
+
+    def test_against_ks(self):
+        rng = np.random.default_rng(8517426291317196949)
+        x = examgrades
+        known_params = {'loc': np.mean(x), 'scale': np.std(x, ddof=1)}
+        res = goodness_of_fit(stats.norm, x, known_params=known_params,
+                              statistic='ks', random_state=rng)
+        ref = stats.kstest(x, stats.norm(**known_params).cdf, method='exact')
+        assert_allclose(res.statistic, ref.statistic)  # ~0.0848
+        assert_allclose(res.pvalue, ref.pvalue, atol=5e-3)  # ~0.335
+
+    def test_against_lilliefors(self):
+        rng = np.random.default_rng(2291803665717442724)
+        x = examgrades
+        res = goodness_of_fit(stats.norm, x, statistic='ks', random_state=rng)
+        known_params = {'loc': np.mean(x), 'scale': np.std(x, ddof=1)}
+        ref = stats.kstest(x, stats.norm(**known_params).cdf, method='exact')
+        assert_allclose(res.statistic, ref.statistic)  # ~0.0848
+        assert_allclose(res.pvalue, 0.0348, atol=5e-3)
+
+    def test_against_cvm(self):
+        rng = np.random.default_rng(8674330857509546614)
+        x = examgrades
+        known_params = {'loc': np.mean(x), 'scale': np.std(x, ddof=1)}
+        res = goodness_of_fit(stats.norm, x, known_params=known_params,
+                              statistic='cvm', random_state=rng)
+        ref = stats.cramervonmises(x, stats.norm(**known_params).cdf)
+        assert_allclose(res.statistic, ref.statistic)  # ~0.090
+        assert_allclose(res.pvalue, ref.pvalue, atol=5e-3)  # ~0.636
+
+    def test_against_anderson_case_0(self):
+        # "Case 0" is where loc and scale are known [1]
+        rng = np.random.default_rng(7384539336846690410)
+        x = np.arange(1, 101)
+        # loc that produced critical value of statistic found w/ root_scalar
+        known_params = {'loc': 45.01575354024957, 'scale': 30}
+        res = goodness_of_fit(stats.norm, x, known_params=known_params,
+                              statistic='ad', random_state=rng)
+        assert_allclose(res.statistic, 2.492)  # See [1] Table 1A 1.0
+        assert_allclose(res.pvalue, 0.05, atol=5e-3)
+
+    def test_against_anderson_case_1(self):
+        # "Case 1" is where scale is known and loc is fit [1]
+        rng = np.random.default_rng(5040212485680146248)
+        x = np.arange(1, 101)
+        # scale that produced critical value of statistic found w/ root_scalar
+        known_params = {'scale': 29.957112639101933}
+        res = goodness_of_fit(stats.norm, x, known_params=known_params,
+                              statistic='ad', random_state=rng)
+        assert_allclose(res.statistic, 0.908)  # See [1] Table 1B 1.1
+        assert_allclose(res.pvalue, 0.1, atol=5e-3)
+
+    def test_against_anderson_case_2(self):
+        # "Case 2" is where loc is known and scale is fit [1]
+        rng = np.random.default_rng(726693985720914083)
+        x = np.arange(1, 101)
+        # loc that produced critical value of statistic found w/ root_scalar
+        known_params = {'loc': 44.5680212261933}
+        res = goodness_of_fit(stats.norm, x, known_params=known_params,
+                              statistic='ad', random_state=rng)
+        assert_allclose(res.statistic, 2.904)  # See [1] Table 1B 1.2
+        assert_allclose(res.pvalue, 0.025, atol=5e-3)
+
+    def test_against_anderson_case_3(self):
+        # "Case 3" is where both loc and scale are fit [1]
+        rng = np.random.default_rng(6763691329830218206)
+        # c that produced critical value of statistic found w/ root_scalar
+        x = stats.skewnorm.rvs(1.4477847789132101, loc=1, scale=2, size=100,
+                               random_state=rng)
+        res = goodness_of_fit(stats.norm, x, statistic='ad', random_state=rng)
+        assert_allclose(res.statistic, 0.559)  # See [1] Table 1B 1.2
+        assert_allclose(res.pvalue, 0.15, atol=5e-3)
+
+    @pytest.mark.xslow
+    def test_against_anderson_gumbel_r(self):
+        rng = np.random.default_rng(7302761058217743)
+        # c that produced critical value of statistic found w/ root_scalar
+        x = stats.genextreme(0.051896837188595134, loc=0.5,
+                             scale=1.5).rvs(size=1000, random_state=rng)
+        res = goodness_of_fit(stats.gumbel_r, x, statistic='ad',
+                              random_state=rng)
+        ref = stats.anderson(x, dist='gumbel_r')
+        assert_allclose(res.statistic, ref.critical_values[0])
+        assert_allclose(res.pvalue, ref.significance_level[0]/100, atol=5e-3)
+
+    def test_against_filliben_norm(self):
+        # Test against `stats.fit` ref. [7] Section 8 "Example"
+        rng = np.random.default_rng(8024266430745011915)
+        y = [6, 1, -4, 8, -2, 5, 0]
+        known_params = {'loc': 0, 'scale': 1}
+        res = stats.goodness_of_fit(stats.norm, y, known_params=known_params,
+                                    statistic="filliben", random_state=rng)
+        # Slight discrepancy presumably due to roundoff in Filliben's
+        # calculation. Using exact order statistic medians instead of
+        # Filliben's approximation doesn't account for it.
+        assert_allclose(res.statistic, 0.98538, atol=1e-4)
+        assert 0.75 < res.pvalue < 0.9
+
+        # Using R's ppcc library:
+        # library(ppcc)
+        # options(digits=16)
+        # x < - c(6, 1, -4, 8, -2, 5, 0)
+        # set.seed(100)
+        # ppccTest(x, "qnorm", ppos="Filliben")
+        # Discrepancy with
+        assert_allclose(res.statistic, 0.98540957187084, rtol=2e-5)
+        assert_allclose(res.pvalue, 0.8875, rtol=2e-3)
+
+    def test_filliben_property(self):
+        # Filliben's statistic should be independent of data location and scale
+        rng = np.random.default_rng(8535677809395478813)
+        x = rng.normal(loc=10, scale=0.5, size=100)
+        res = stats.goodness_of_fit(stats.norm, x,
+                                    statistic="filliben", random_state=rng)
+        known_params = {'loc': 0, 'scale': 1}
+        ref = stats.goodness_of_fit(stats.norm, x, known_params=known_params,
+                                    statistic="filliben", random_state=rng)
+        assert_allclose(res.statistic, ref.statistic, rtol=1e-15)
+
+    @pytest.mark.parametrize('case', [(25, [.928, .937, .950, .958, .966]),
+                                      (50, [.959, .965, .972, .977, .981]),
+                                      (95, [.977, .979, .983, .986, .989])])
+    def test_against_filliben_norm_table(self, case):
+        # Test against `stats.fit` ref. [7] Table 1
+        rng = np.random.default_rng(504569995557928957)
+        n, ref = case
+        x = rng.random(n)
+        known_params = {'loc': 0, 'scale': 1}
+        res = stats.goodness_of_fit(stats.norm, x, known_params=known_params,
+                                    statistic="filliben", random_state=rng)
+        percentiles = np.array([0.005, 0.01, 0.025, 0.05, 0.1])
+        res = stats.scoreatpercentile(res.null_distribution, percentiles*100)
+        assert_allclose(res, ref, atol=2e-3)
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize('case', [(5, 0.95772790260469, 0.4755),
+                                      (6, 0.95398832257958, 0.3848),
+                                      (7, 0.9432692889277, 0.2328)])
+    def test_against_ppcc(self, case):
+        # Test against R ppcc, e.g.
+        # library(ppcc)
+        # options(digits=16)
+        # x < - c(0.52325412, 1.06907699, -0.36084066, 0.15305959, 0.99093194)
+        # set.seed(100)
+        # ppccTest(x, "qrayleigh", ppos="Filliben")
+        n, ref_statistic, ref_pvalue = case
+        rng = np.random.default_rng(7777775561439803116)
+        x = rng.normal(size=n)
+        res = stats.goodness_of_fit(stats.rayleigh, x, statistic="filliben",
+                                    random_state=rng)
+        assert_allclose(res.statistic, ref_statistic, rtol=1e-4)
+        assert_allclose(res.pvalue, ref_pvalue, atol=1.5e-2)
+
+    def test_params_effects(self):
+        # Ensure that `guessed_params`, `fit_params`, and `known_params` have
+        # the intended effects.
+        rng = np.random.default_rng(9121950977643805391)
+        x = stats.skewnorm.rvs(-5.044559778383153, loc=1, scale=2, size=50,
+                               random_state=rng)
+
+        # Show that `guessed_params` don't fit to the guess,
+        # but `fit_params` and `known_params` respect the provided fit
+        guessed_params = {'c': 13.4}
+        fit_params = {'scale': 13.73}
+        known_params = {'loc': -13.85}
+        rng = np.random.default_rng(9121950977643805391)
+        res1 = goodness_of_fit(stats.weibull_min, x, n_mc_samples=2,
+                               guessed_params=guessed_params,
+                               fit_params=fit_params,
+                               known_params=known_params, random_state=rng)
+        assert not np.allclose(res1.fit_result.params.c, 13.4)
+        assert_equal(res1.fit_result.params.scale, 13.73)
+        assert_equal(res1.fit_result.params.loc, -13.85)
+
+        # Show that changing the guess changes the parameter that gets fit,
+        # and it changes the null distribution
+        guessed_params = {'c': 2}
+        rng = np.random.default_rng(9121950977643805391)
+        res2 = goodness_of_fit(stats.weibull_min, x, n_mc_samples=2,
+                               guessed_params=guessed_params,
+                               fit_params=fit_params,
+                               known_params=known_params, random_state=rng)
+        assert not np.allclose(res2.fit_result.params.c,
+                               res1.fit_result.params.c, rtol=1e-8)
+        assert not np.allclose(res2.null_distribution,
+                               res1.null_distribution, rtol=1e-8)
+        assert_equal(res2.fit_result.params.scale, 13.73)
+        assert_equal(res2.fit_result.params.loc, -13.85)
+
+        # If we set all parameters as fit_params and known_params,
+        # they're all fixed to those values, but the null distribution
+        # varies.
+        fit_params = {'c': 13.4, 'scale': 13.73}
+        rng = np.random.default_rng(9121950977643805391)
+        res3 = goodness_of_fit(stats.weibull_min, x, n_mc_samples=2,
+                               guessed_params=guessed_params,
+                               fit_params=fit_params,
+                               known_params=known_params, random_state=rng)
+        assert_equal(res3.fit_result.params.c, 13.4)
+        assert_equal(res3.fit_result.params.scale, 13.73)
+        assert_equal(res3.fit_result.params.loc, -13.85)
+        assert not np.allclose(res3.null_distribution, res1.null_distribution)
+
+    def test_custom_statistic(self):
+        # Test support for custom statistic function.
+
+        # References:
+        # [1] Pyke, R. (1965).  "Spacings".  Journal of the Royal Statistical
+        #     Society: Series B (Methodological), 27(3): 395-436.
+        # [2] Burrows, P. M. (1979).  "Selected Percentage Points of
+        #     Greenwood's Statistics".  Journal of the Royal Statistical
+        #     Society. Series A (General), 142(2): 256-258.
+
+        # Use the Greenwood statistic for illustration; see [1, p.402].
+        def greenwood(dist, data, *, axis):
+            x = np.sort(data, axis=axis)
+            y = dist.cdf(x)
+            d = np.diff(y, axis=axis, prepend=0, append=1)
+            return np.sum(d ** 2, axis=axis)
+
+        # Run the Monte Carlo test with sample size = 5 on a fully specified
+        # null distribution, and compare the simulated quantiles to the exact
+        # ones given in [2, Table 1, column (n = 5)].
+        rng = np.random.default_rng(9121950977643805391)
+        data = stats.expon.rvs(size=5, random_state=rng)
+        result = goodness_of_fit(stats.expon, data,
+                                 known_params={'loc': 0, 'scale': 1},
+                                 statistic=greenwood, random_state=rng)
+        p = [.01, .05, .1, .2, .3, .4, .5, .6, .7, .8, .9, .95, .99]
+        exact_quantiles = [
+            .183863, .199403, .210088, .226040, .239947, .253677, .268422,
+            .285293, .306002, .334447, .382972, .432049, .547468]
+        simulated_quantiles = np.quantile(result.null_distribution, p)
+        assert_allclose(simulated_quantiles, exact_quantiles, atol=0.005)
+
+class TestFitResult:
+    def test_plot_iv(self):
+        rng = np.random.default_rng(1769658657308472721)
+        data = stats.norm.rvs(0, 1, size=100, random_state=rng)
+
+        def optimizer(*args, **kwargs):
+            return differential_evolution(*args, **kwargs, seed=rng)
+
+        bounds = [(0, 30), (0, 1)]
+        res = stats.fit(stats.norm, data, bounds, optimizer=optimizer)
+        try:
+            import matplotlib  # noqa: F401
+            message = r"`plot_type` must be one of \{'..."
+            with pytest.raises(ValueError, match=message):
+                res.plot(plot_type='llama')
+        except (ModuleNotFoundError, ImportError):
+            # Avoid trying to call MPL with numpy 2.0-dev, because that fails
+            # too often due to ABI mismatches and is hard to avoid. This test
+            # will work fine again once MPL has done a 2.0-compatible release.
+            if not np.__version__.startswith('2.0.0.dev0'):
+                message = r"matplotlib must be installed to use method `plot`."
+                with pytest.raises(ModuleNotFoundError, match=message):
+                    res.plot(plot_type='llama')

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_hypotests.py

@@ -0,0 +1,1857 @@
+from itertools import product
+
+import numpy as np
+import random
+import functools
+import pytest
+from numpy.testing import (assert_, assert_equal, assert_allclose,
+                           assert_almost_equal)  # avoid new uses
+from pytest import raises as assert_raises
+
+import scipy.stats as stats
+from scipy.stats import distributions
+from scipy.stats._hypotests import (epps_singleton_2samp, cramervonmises,
+                                    _cdf_cvm, cramervonmises_2samp,
+                                    _pval_cvm_2samp_exact, barnard_exact,
+                                    boschloo_exact)
+from scipy.stats._mannwhitneyu import mannwhitneyu, _mwu_state
+from .common_tests import check_named_results
+from scipy._lib._testutils import _TestPythranFunc
+from scipy.stats._axis_nan_policy import SmallSampleWarning, too_small_1d_not_omit
+
+
+class TestEppsSingleton:
+    def test_statistic_1(self):
+        # first example in Goerg & Kaiser, also in original paper of
+        # Epps & Singleton. Note: values do not match exactly, the
+        # value of the interquartile range varies depending on how
+        # quantiles are computed
+        x = np.array([-0.35, 2.55, 1.73, 0.73, 0.35,
+                      2.69, 0.46, -0.94, -0.37, 12.07])
+        y = np.array([-1.15, -0.15, 2.48, 3.25, 3.71,
+                      4.29, 5.00, 7.74, 8.38, 8.60])
+        w, p = epps_singleton_2samp(x, y)
+        assert_almost_equal(w, 15.14, decimal=1)
+        assert_almost_equal(p, 0.00442, decimal=3)
+
+    def test_statistic_2(self):
+        # second example in Goerg & Kaiser, again not a perfect match
+        x = np.array((0, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 5, 5, 5, 6, 10,
+                      10, 10, 10))
+        y = np.array((10, 4, 0, 5, 10, 10, 0, 5, 6, 7, 10, 3, 1, 7, 0, 8, 1,
+                      5, 8, 10))
+        w, p = epps_singleton_2samp(x, y)
+        assert_allclose(w, 8.900, atol=0.001)
+        assert_almost_equal(p, 0.06364, decimal=3)
+
+    def test_epps_singleton_array_like(self):
+        np.random.seed(1234)
+        x, y = np.arange(30), np.arange(28)
+
+        w1, p1 = epps_singleton_2samp(list(x), list(y))
+        w2, p2 = epps_singleton_2samp(tuple(x), tuple(y))
+        w3, p3 = epps_singleton_2samp(x, y)
+
+        assert_(w1 == w2 == w3)
+        assert_(p1 == p2 == p3)
+
+    def test_epps_singleton_size(self):
+        # warns if sample contains fewer than 5 elements
+        x, y = (1, 2, 3, 4), np.arange(10)
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = epps_singleton_2samp(x, y)
+            assert_equal(res.statistic, np.nan)
+            assert_equal(res.pvalue, np.nan)
+
+    def test_epps_singleton_nonfinite(self):
+        # raise error if there are non-finite values
+        x, y = (1, 2, 3, 4, 5, np.inf), np.arange(10)
+        assert_raises(ValueError, epps_singleton_2samp, x, y)
+
+    def test_names(self):
+        x, y = np.arange(20), np.arange(30)
+        res = epps_singleton_2samp(x, y)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes)
+
+
+class TestCvm:
+    # the expected values of the cdfs are taken from Table 1 in
+    # Csorgo / Faraway: The Exact and Asymptotic Distribution of
+    # Cramér-von Mises Statistics, 1996.
+    def test_cdf_4(self):
+        assert_allclose(
+                _cdf_cvm([0.02983, 0.04111, 0.12331, 0.94251], 4),
+                [0.01, 0.05, 0.5, 0.999],
+                atol=1e-4)
+
+    def test_cdf_10(self):
+        assert_allclose(
+                _cdf_cvm([0.02657, 0.03830, 0.12068, 0.56643], 10),
+                [0.01, 0.05, 0.5, 0.975],
+                atol=1e-4)
+
+    def test_cdf_1000(self):
+        assert_allclose(
+                _cdf_cvm([0.02481, 0.03658, 0.11889, 1.16120], 1000),
+                [0.01, 0.05, 0.5, 0.999],
+                atol=1e-4)
+
+    def test_cdf_inf(self):
+        assert_allclose(
+                _cdf_cvm([0.02480, 0.03656, 0.11888, 1.16204]),
+                [0.01, 0.05, 0.5, 0.999],
+                atol=1e-4)
+
+    def test_cdf_support(self):
+        # cdf has support on [1/(12*n), n/3]
+        assert_equal(_cdf_cvm([1/(12*533), 533/3], 533), [0, 1])
+        assert_equal(_cdf_cvm([1/(12*(27 + 1)), (27 + 1)/3], 27), [0, 1])
+
+    def test_cdf_large_n(self):
+        # test that asymptotic cdf and cdf for large samples are close
+        assert_allclose(
+                _cdf_cvm([0.02480, 0.03656, 0.11888, 1.16204, 100], 10000),
+                _cdf_cvm([0.02480, 0.03656, 0.11888, 1.16204, 100]),
+                atol=1e-4)
+
+    def test_large_x(self):
+        # for large values of x and n, the series used to compute the cdf
+        # converges slowly.
+        # this leads to bug in R package goftest and MAPLE code that is
+        # the basis of the implementation in scipy
+        # note: cdf = 1 for x >= 1000/3 and n = 1000
+        assert_(0.99999 < _cdf_cvm(333.3, 1000) < 1.0)
+        assert_(0.99999 < _cdf_cvm(333.3) < 1.0)
+
+    def test_low_p(self):
+        # _cdf_cvm can return values larger than 1. In that case, we just
+        # return a p-value of zero.
+        n = 12
+        res = cramervonmises(np.ones(n)*0.8, 'norm')
+        assert_(_cdf_cvm(res.statistic, n) > 1.0)
+        assert_equal(res.pvalue, 0)
+
+    @pytest.mark.parametrize('x', [(), [1.5]])
+    def test_invalid_input(self, x):
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = cramervonmises(x, "norm")
+            assert_equal(res.statistic, np.nan)
+            assert_equal(res.pvalue, np.nan)
+
+    def test_values_R(self):
+        # compared against R package goftest, version 1.1.1
+        # goftest::cvm.test(c(-1.7, 2, 0, 1.3, 4, 0.1, 0.6), "pnorm")
+        res = cramervonmises([-1.7, 2, 0, 1.3, 4, 0.1, 0.6], "norm")
+        assert_allclose(res.statistic, 0.288156, atol=1e-6)
+        assert_allclose(res.pvalue, 0.1453465, atol=1e-6)
+
+        # goftest::cvm.test(c(-1.7, 2, 0, 1.3, 4, 0.1, 0.6),
+        #                   "pnorm", mean = 3, sd = 1.5)
+        res = cramervonmises([-1.7, 2, 0, 1.3, 4, 0.1, 0.6], "norm", (3, 1.5))
+        assert_allclose(res.statistic, 0.9426685, atol=1e-6)
+        assert_allclose(res.pvalue, 0.002026417, atol=1e-6)
+
+        # goftest::cvm.test(c(1, 2, 5, 1.4, 0.14, 11, 13, 0.9, 7.5), "pexp")
+        res = cramervonmises([1, 2, 5, 1.4, 0.14, 11, 13, 0.9, 7.5], "expon")
+        assert_allclose(res.statistic, 0.8421854, atol=1e-6)
+        assert_allclose(res.pvalue, 0.004433406, atol=1e-6)
+
+    def test_callable_cdf(self):
+        x, args = np.arange(5), (1.4, 0.7)
+        r1 = cramervonmises(x, distributions.expon.cdf)
+        r2 = cramervonmises(x, "expon")
+        assert_equal((r1.statistic, r1.pvalue), (r2.statistic, r2.pvalue))
+
+        r1 = cramervonmises(x, distributions.beta.cdf, args)
+        r2 = cramervonmises(x, "beta", args)
+        assert_equal((r1.statistic, r1.pvalue), (r2.statistic, r2.pvalue))
+
+
+class TestMannWhitneyU:
+
+    # All magic numbers are from R wilcox.test unless otherwise specified
+    # https://rdrr.io/r/stats/wilcox.test.html
+
+    # --- Test Input Validation ---
+
+    @pytest.mark.parametrize('kwargs_update', [{'x': []}, {'y': []},
+                                               {'x': [], 'y': []}])
+    def test_empty(self, kwargs_update):
+        x = np.array([1, 2])  # generic, valid inputs
+        y = np.array([3, 4])
+        kwargs = dict(x=x, y=y)
+        kwargs.update(kwargs_update)
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = mannwhitneyu(**kwargs)
+            assert_equal(res.statistic, np.nan)
+            assert_equal(res.pvalue, np.nan)
+
+    def test_input_validation(self):
+        x = np.array([1, 2])  # generic, valid inputs
+        y = np.array([3, 4])
+        with assert_raises(ValueError, match="`use_continuity` must be one"):
+            mannwhitneyu(x, y, use_continuity='ekki')
+        with assert_raises(ValueError, match="`alternative` must be one of"):
+            mannwhitneyu(x, y, alternative='ekki')
+        with assert_raises(ValueError, match="`axis` must be an integer"):
+            mannwhitneyu(x, y, axis=1.5)
+        with assert_raises(ValueError, match="`method` must be one of"):
+            mannwhitneyu(x, y, method='ekki')
+
+    def test_auto(self):
+        # Test that default method ('auto') chooses intended method
+
+        np.random.seed(1)
+        n = 8  # threshold to switch from exact to asymptotic
+
+        # both inputs are smaller than threshold; should use exact
+        x = np.random.rand(n-1)
+        y = np.random.rand(n-1)
+        auto = mannwhitneyu(x, y)
+        asymptotic = mannwhitneyu(x, y, method='asymptotic')
+        exact = mannwhitneyu(x, y, method='exact')
+        assert auto.pvalue == exact.pvalue
+        assert auto.pvalue != asymptotic.pvalue
+
+        # one input is smaller than threshold; should use exact
+        x = np.random.rand(n-1)
+        y = np.random.rand(n+1)
+        auto = mannwhitneyu(x, y)
+        asymptotic = mannwhitneyu(x, y, method='asymptotic')
+        exact = mannwhitneyu(x, y, method='exact')
+        assert auto.pvalue == exact.pvalue
+        assert auto.pvalue != asymptotic.pvalue
+
+        # other input is smaller than threshold; should use exact
+        auto = mannwhitneyu(y, x)
+        asymptotic = mannwhitneyu(x, y, method='asymptotic')
+        exact = mannwhitneyu(x, y, method='exact')
+        assert auto.pvalue == exact.pvalue
+        assert auto.pvalue != asymptotic.pvalue
+
+        # both inputs are larger than threshold; should use asymptotic
+        x = np.random.rand(n+1)
+        y = np.random.rand(n+1)
+        auto = mannwhitneyu(x, y)
+        asymptotic = mannwhitneyu(x, y, method='asymptotic')
+        exact = mannwhitneyu(x, y, method='exact')
+        assert auto.pvalue != exact.pvalue
+        assert auto.pvalue == asymptotic.pvalue
+
+        # both inputs are smaller than threshold, but there is a tie
+        # should use asymptotic
+        x = np.random.rand(n-1)
+        y = np.random.rand(n-1)
+        y[3] = x[3]
+        auto = mannwhitneyu(x, y)
+        asymptotic = mannwhitneyu(x, y, method='asymptotic')
+        exact = mannwhitneyu(x, y, method='exact')
+        assert auto.pvalue != exact.pvalue
+        assert auto.pvalue == asymptotic.pvalue
+
+    # --- Test Basic Functionality ---
+
+    x = [210.052110, 110.190630, 307.918612]
+    y = [436.08811482466416, 416.37397329768191, 179.96975939463582,
+         197.8118754228619, 34.038757281225756, 138.54220550921517,
+         128.7769351470246, 265.92721427951852, 275.6617533155341,
+         592.34083395416258, 448.73177590617018, 300.61495185038905,
+         187.97508449019588]
+
+    # This test was written for mann_whitney_u in gh-4933.
+    # Originally, the p-values for alternatives were swapped;
+    # this has been corrected and the tests have been refactored for
+    # compactness, but otherwise the tests are unchanged.
+    # R code for comparison, e.g.:
+    # options(digits = 16)
+    # x = c(210.052110, 110.190630, 307.918612)
+    # y = c(436.08811482466416, 416.37397329768191, 179.96975939463582,
+    #       197.8118754228619, 34.038757281225756, 138.54220550921517,
+    #       128.7769351470246, 265.92721427951852, 275.6617533155341,
+    #       592.34083395416258, 448.73177590617018, 300.61495185038905,
+    #       187.97508449019588)
+    # wilcox.test(x, y, alternative="g", exact=TRUE)
+    cases_basic = [[{"alternative": 'two-sided', "method": "asymptotic"},
+                    (16, 0.6865041817876)],
+                   [{"alternative": 'less', "method": "asymptotic"},
+                    (16, 0.3432520908938)],
+                   [{"alternative": 'greater', "method": "asymptotic"},
+                    (16, 0.7047591913255)],
+                   [{"alternative": 'two-sided', "method": "exact"},
+                    (16, 0.7035714285714)],
+                   [{"alternative": 'less', "method": "exact"},
+                    (16, 0.3517857142857)],
+                   [{"alternative": 'greater', "method": "exact"},
+                    (16, 0.6946428571429)]]
+
+    @pytest.mark.parametrize(("kwds", "expected"), cases_basic)
+    def test_basic(self, kwds, expected):
+        res = mannwhitneyu(self.x, self.y, **kwds)
+        assert_allclose(res, expected)
+
+    cases_continuity = [[{"alternative": 'two-sided', "use_continuity": True},
+                         (23, 0.6865041817876)],
+                        [{"alternative": 'less', "use_continuity": True},
+                         (23, 0.7047591913255)],
+                        [{"alternative": 'greater', "use_continuity": True},
+                         (23, 0.3432520908938)],
+                        [{"alternative": 'two-sided', "use_continuity": False},
+                         (23, 0.6377328900502)],
+                        [{"alternative": 'less', "use_continuity": False},
+                         (23, 0.6811335549749)],
+                        [{"alternative": 'greater', "use_continuity": False},
+                         (23, 0.3188664450251)]]
+
+    @pytest.mark.parametrize(("kwds", "expected"), cases_continuity)
+    def test_continuity(self, kwds, expected):
+        # When x and y are interchanged, less and greater p-values should
+        # swap (compare to above). This wouldn't happen if the continuity
+        # correction were applied in the wrong direction. Note that less and
+        # greater p-values do not sum to 1 when continuity correction is on,
+        # which is what we'd expect. Also check that results match R when
+        # continuity correction is turned off.
+        # Note that method='asymptotic' -> exact=FALSE
+        # and use_continuity=False -> correct=FALSE, e.g.:
+        # wilcox.test(x, y, alternative="t", exact=FALSE, correct=FALSE)
+        res = mannwhitneyu(self.y, self.x, method='asymptotic', **kwds)
+        assert_allclose(res, expected)
+
+    def test_tie_correct(self):
+        # Test tie correction against R's wilcox.test
+        # options(digits = 16)
+        # x = c(1, 2, 3, 4)
+        # y = c(1, 2, 3, 4, 5)
+        # wilcox.test(x, y, exact=FALSE)
+        x = [1, 2, 3, 4]
+        y0 = np.array([1, 2, 3, 4, 5])
+        dy = np.array([0, 1, 0, 1, 0])*0.01
+        dy2 = np.array([0, 0, 1, 0, 0])*0.01
+        y = [y0-0.01, y0-dy, y0-dy2, y0, y0+dy2, y0+dy, y0+0.01]
+        res = mannwhitneyu(x, y, axis=-1, method="asymptotic")
+        U_expected = [10, 9, 8.5, 8, 7.5, 7, 6]
+        p_expected = [1, 0.9017048037317, 0.804080657472, 0.7086240584439,
+                      0.6197963884941, 0.5368784563079, 0.3912672792826]
+        assert_equal(res.statistic, U_expected)
+        assert_allclose(res.pvalue, p_expected)
+
+    # --- Test Exact Distribution of U ---
+
+    # These are tabulated values of the CDF of the exact distribution of
+    # the test statistic from pg 52 of reference [1] (Mann-Whitney Original)
+    pn3 = {1: [0.25, 0.5, 0.75], 2: [0.1, 0.2, 0.4, 0.6],
+           3: [0.05, .1, 0.2, 0.35, 0.5, 0.65]}
+    pn4 = {1: [0.2, 0.4, 0.6], 2: [0.067, 0.133, 0.267, 0.4, 0.6],
+           3: [0.028, 0.057, 0.114, 0.2, .314, 0.429, 0.571],
+           4: [0.014, 0.029, 0.057, 0.1, 0.171, 0.243, 0.343, 0.443, 0.557]}
+    pm5 = {1: [0.167, 0.333, 0.5, 0.667],
+           2: [0.047, 0.095, 0.19, 0.286, 0.429, 0.571],
+           3: [0.018, 0.036, 0.071, 0.125, 0.196, 0.286, 0.393, 0.5, 0.607],
+           4: [0.008, 0.016, 0.032, 0.056, 0.095, 0.143,
+               0.206, 0.278, 0.365, 0.452, 0.548],
+           5: [0.004, 0.008, 0.016, 0.028, 0.048, 0.075, 0.111,
+               0.155, 0.21, 0.274, 0.345, .421, 0.5, 0.579]}
+    pm6 = {1: [0.143, 0.286, 0.428, 0.571],
+           2: [0.036, 0.071, 0.143, 0.214, 0.321, 0.429, 0.571],
+           3: [0.012, 0.024, 0.048, 0.083, 0.131,
+               0.19, 0.274, 0.357, 0.452, 0.548],
+           4: [0.005, 0.01, 0.019, 0.033, 0.057, 0.086, 0.129,
+               0.176, 0.238, 0.305, 0.381, 0.457, 0.543],  # the last element
+           # of the previous list, 0.543, has been modified from 0.545;
+           # I assume it was a typo
+           5: [0.002, 0.004, 0.009, 0.015, 0.026, 0.041, 0.063, 0.089,
+               0.123, 0.165, 0.214, 0.268, 0.331, 0.396, 0.465, 0.535],
+           6: [0.001, 0.002, 0.004, 0.008, 0.013, 0.021, 0.032, 0.047,
+               0.066, 0.09, 0.12, 0.155, 0.197, 0.242, 0.294, 0.350,
+               0.409, 0.469, 0.531]}
+
+    def test_exact_distribution(self):
+        # I considered parametrize. I decided against it.
+        p_tables = {3: self.pn3, 4: self.pn4, 5: self.pm5, 6: self.pm6}
+        for n, table in p_tables.items():
+            for m, p in table.items():
+                # check p-value against table
+                u = np.arange(0, len(p))
+                _mwu_state.set_shapes(m, n)
+                assert_allclose(_mwu_state.cdf(k=u), p, atol=1e-3)
+
+                # check identity CDF + SF - PMF = 1
+                # ( In this implementation, SF(U) includes PMF(U) )
+                u2 = np.arange(0, m*n+1)
+                assert_allclose(_mwu_state.cdf(k=u2)
+                                + _mwu_state.sf(k=u2)
+                                - _mwu_state.pmf(k=u2), 1)
+
+                # check symmetry about mean of U, i.e. pmf(U) = pmf(m*n-U)
+                pmf = _mwu_state.pmf(k=u2)
+                assert_allclose(pmf, pmf[::-1])
+
+                # check symmetry w.r.t. interchange of m, n
+                _mwu_state.set_shapes(n, m)
+                pmf2 = _mwu_state.pmf(k=u2)
+                assert_allclose(pmf, pmf2)
+
+    def test_asymptotic_behavior(self):
+        np.random.seed(0)
+
+        # for small samples, the asymptotic test is not very accurate
+        x = np.random.rand(5)
+        y = np.random.rand(5)
+        res1 = mannwhitneyu(x, y, method="exact")
+        res2 = mannwhitneyu(x, y, method="asymptotic")
+        assert res1.statistic == res2.statistic
+        assert np.abs(res1.pvalue - res2.pvalue) > 1e-2
+
+        # for large samples, they agree reasonably well
+        x = np.random.rand(40)
+        y = np.random.rand(40)
+        res1 = mannwhitneyu(x, y, method="exact")
+        res2 = mannwhitneyu(x, y, method="asymptotic")
+        assert res1.statistic == res2.statistic
+        assert np.abs(res1.pvalue - res2.pvalue) < 1e-3
+
+    # --- Test Corner Cases ---
+
+    def test_exact_U_equals_mean(self):
+        # Test U == m*n/2 with exact method
+        # Without special treatment, two-sided p-value > 1 because both
+        # one-sided p-values are > 0.5
+        res_l = mannwhitneyu([1, 2, 3], [1.5, 2.5], alternative="less",
+                             method="exact")
+        res_g = mannwhitneyu([1, 2, 3], [1.5, 2.5], alternative="greater",
+                             method="exact")
+        assert_equal(res_l.pvalue, res_g.pvalue)
+        assert res_l.pvalue > 0.5
+
+        res = mannwhitneyu([1, 2, 3], [1.5, 2.5], alternative="two-sided",
+                           method="exact")
+        assert_equal(res, (3, 1))
+        # U == m*n/2 for asymptotic case tested in test_gh_2118
+        # The reason it's tricky for the asymptotic test has to do with
+        # continuity correction.
+
+    cases_scalar = [[{"alternative": 'two-sided', "method": "asymptotic"},
+                     (0, 1)],
+                    [{"alternative": 'less', "method": "asymptotic"},
+                     (0, 0.5)],
+                    [{"alternative": 'greater', "method": "asymptotic"},
+                     (0, 0.977249868052)],
+                    [{"alternative": 'two-sided', "method": "exact"}, (0, 1)],
+                    [{"alternative": 'less', "method": "exact"}, (0, 0.5)],
+                    [{"alternative": 'greater', "method": "exact"}, (0, 1)]]
+
+    @pytest.mark.parametrize(("kwds", "result"), cases_scalar)
+    def test_scalar_data(self, kwds, result):
+        # just making sure scalars work
+        assert_allclose(mannwhitneyu(1, 2, **kwds), result)
+
+    def test_equal_scalar_data(self):
+        # when two scalars are equal, there is an -0.5/0 in the asymptotic
+        # approximation. R gives pvalue=1.0 for alternatives 'less' and
+        # 'greater' but NA for 'two-sided'. I don't see why, so I don't
+        # see a need for a special case to match that behavior.
+        assert_equal(mannwhitneyu(1, 1, method="exact"), (0.5, 1))
+        assert_equal(mannwhitneyu(1, 1, method="asymptotic"), (0.5, 1))
+
+        # without continuity correction, this becomes 0/0, which really
+        # is undefined
+        assert_equal(mannwhitneyu(1, 1, method="asymptotic",
+                                  use_continuity=False), (0.5, np.nan))
+
+    # --- Test Enhancements / Bug Reports ---
+
+    @pytest.mark.parametrize("method", ["asymptotic", "exact"])
+    def test_gh_12837_11113(self, method):
+        # Test that behavior for broadcastable nd arrays is appropriate:
+        # output shape is correct and all values are equal to when the test
+        # is performed on one pair of samples at a time.
+        # Tests that gh-12837 and gh-11113 (requests for n-d input)
+        # are resolved
+        np.random.seed(0)
+
+        # arrays are broadcastable except for axis = -3
+        axis = -3
+        m, n = 7, 10  # sample sizes
+        x = np.random.rand(m, 3, 8)
+        y = np.random.rand(6, n, 1, 8) + 0.1
+        res = mannwhitneyu(x, y, method=method, axis=axis)
+
+        shape = (6, 3, 8)  # appropriate shape of outputs, given inputs
+        assert res.pvalue.shape == shape
+        assert res.statistic.shape == shape
+
+        # move axis of test to end for simplicity
+        x, y = np.moveaxis(x, axis, -1), np.moveaxis(y, axis, -1)
+
+        x = x[None, ...]  # give x a zeroth dimension
+        assert x.ndim == y.ndim
+
+        x = np.broadcast_to(x, shape + (m,))
+        y = np.broadcast_to(y, shape + (n,))
+        assert x.shape[:-1] == shape
+        assert y.shape[:-1] == shape
+
+        # loop over pairs of samples
+        statistics = np.zeros(shape)
+        pvalues = np.zeros(shape)
+        for indices in product(*[range(i) for i in shape]):
+            xi = x[indices]
+            yi = y[indices]
+            temp = mannwhitneyu(xi, yi, method=method)
+            statistics[indices] = temp.statistic
+            pvalues[indices] = temp.pvalue
+
+        np.testing.assert_equal(res.pvalue, pvalues)
+        np.testing.assert_equal(res.statistic, statistics)
+
+    def test_gh_11355(self):
+        # Test for correct behavior with NaN/Inf in input
+        x = [1, 2, 3, 4]
+        y = [3, 6, 7, 8, 9, 3, 2, 1, 4, 4, 5]
+        res1 = mannwhitneyu(x, y)
+
+        # Inf is not a problem. This is a rank test, and it's the largest value
+        y[4] = np.inf
+        res2 = mannwhitneyu(x, y)
+
+        assert_equal(res1.statistic, res2.statistic)
+        assert_equal(res1.pvalue, res2.pvalue)
+
+        # NaNs should propagate by default.
+        y[4] = np.nan
+        res3 = mannwhitneyu(x, y)
+        assert_equal(res3.statistic, np.nan)
+        assert_equal(res3.pvalue, np.nan)
+
+    cases_11355 = [([1, 2, 3, 4],
+                    [3, 6, 7, 8, np.inf, 3, 2, 1, 4, 4, 5],
+                    10, 0.1297704873477),
+                   ([1, 2, 3, 4],
+                    [3, 6, 7, 8, np.inf, np.inf, 2, 1, 4, 4, 5],
+                    8.5, 0.08735617507695),
+                   ([1, 2, np.inf, 4],
+                    [3, 6, 7, 8, np.inf, 3, 2, 1, 4, 4, 5],
+                    17.5, 0.5988856695752),
+                   ([1, 2, np.inf, 4],
+                    [3, 6, 7, 8, np.inf, np.inf, 2, 1, 4, 4, 5],
+                    16, 0.4687165824462),
+                   ([1, np.inf, np.inf, 4],
+                    [3, 6, 7, 8, np.inf, np.inf, 2, 1, 4, 4, 5],
+                    24.5, 0.7912517950119)]
+
+    @pytest.mark.parametrize(("x", "y", "statistic", "pvalue"), cases_11355)
+    def test_gh_11355b(self, x, y, statistic, pvalue):
+        # Test for correct behavior with NaN/Inf in input
+        res = mannwhitneyu(x, y, method='asymptotic')
+        assert_allclose(res.statistic, statistic, atol=1e-12)
+        assert_allclose(res.pvalue, pvalue, atol=1e-12)
+
+    cases_9184 = [[True, "less", "asymptotic", 0.900775348204],
+                  [True, "greater", "asymptotic", 0.1223118025635],
+                  [True, "two-sided", "asymptotic", 0.244623605127],
+                  [False, "less", "asymptotic", 0.8896643190401],
+                  [False, "greater", "asymptotic", 0.1103356809599],
+                  [False, "two-sided", "asymptotic", 0.2206713619198],
+                  [True, "less", "exact", 0.8967698967699],
+                  [True, "greater", "exact", 0.1272061272061],
+                  [True, "two-sided", "exact", 0.2544122544123]]
+
+    @pytest.mark.parametrize(("use_continuity", "alternative",
+                              "method", "pvalue_exp"), cases_9184)
+    def test_gh_9184(self, use_continuity, alternative, method, pvalue_exp):
+        # gh-9184 might be considered a doc-only bug. Please see the
+        # documentation to confirm that mannwhitneyu correctly notes
+        # that the output statistic is that of the first sample (x). In any
+        # case, check the case provided there against output from R.
+        # R code:
+        # options(digits=16)
+        # x <- c(0.80, 0.83, 1.89, 1.04, 1.45, 1.38, 1.91, 1.64, 0.73, 1.46)
+        # y <- c(1.15, 0.88, 0.90, 0.74, 1.21)
+        # wilcox.test(x, y, alternative = "less", exact = FALSE)
+        # wilcox.test(x, y, alternative = "greater", exact = FALSE)
+        # wilcox.test(x, y, alternative = "two.sided", exact = FALSE)
+        # wilcox.test(x, y, alternative = "less", exact = FALSE,
+        #             correct=FALSE)
+        # wilcox.test(x, y, alternative = "greater", exact = FALSE,
+        #             correct=FALSE)
+        # wilcox.test(x, y, alternative = "two.sided", exact = FALSE,
+        #             correct=FALSE)
+        # wilcox.test(x, y, alternative = "less", exact = TRUE)
+        # wilcox.test(x, y, alternative = "greater", exact = TRUE)
+        # wilcox.test(x, y, alternative = "two.sided", exact = TRUE)
+        statistic_exp = 35
+        x = (0.80, 0.83, 1.89, 1.04, 1.45, 1.38, 1.91, 1.64, 0.73, 1.46)
+        y = (1.15, 0.88, 0.90, 0.74, 1.21)
+        res = mannwhitneyu(x, y, use_continuity=use_continuity,
+                           alternative=alternative, method=method)
+        assert_equal(res.statistic, statistic_exp)
+        assert_allclose(res.pvalue, pvalue_exp)
+
+    def test_gh_4067(self):
+        # Test for correct behavior with all NaN input - default is propagate
+        a = np.array([np.nan, np.nan, np.nan, np.nan, np.nan])
+        b = np.array([np.nan, np.nan, np.nan, np.nan, np.nan])
+        res = mannwhitneyu(a, b)
+        assert_equal(res.statistic, np.nan)
+        assert_equal(res.pvalue, np.nan)
+
+    # All cases checked against R wilcox.test, e.g.
+    # options(digits=16)
+    # x = c(1, 2, 3)
+    # y = c(1.5, 2.5)
+    # wilcox.test(x, y, exact=FALSE, alternative='less')
+
+    cases_2118 = [[[1, 2, 3], [1.5, 2.5], "greater", (3, 0.6135850036578)],
+                  [[1, 2, 3], [1.5, 2.5], "less", (3, 0.6135850036578)],
+                  [[1, 2, 3], [1.5, 2.5], "two-sided", (3, 1.0)],
+                  [[1, 2, 3], [2], "greater", (1.5, 0.681324055883)],
+                  [[1, 2, 3], [2], "less", (1.5, 0.681324055883)],
+                  [[1, 2, 3], [2], "two-sided", (1.5, 1)],
+                  [[1, 2], [1, 2], "greater", (2, 0.667497228949)],
+                  [[1, 2], [1, 2], "less", (2, 0.667497228949)],
+                  [[1, 2], [1, 2], "two-sided", (2, 1)]]
+
+    @pytest.mark.parametrize(["x", "y", "alternative", "expected"], cases_2118)
+    def test_gh_2118(self, x, y, alternative, expected):
+        # test cases in which U == m*n/2 when method is asymptotic
+        # applying continuity correction could result in p-value > 1
+        res = mannwhitneyu(x, y, use_continuity=True, alternative=alternative,
+                           method="asymptotic")
+        assert_allclose(res, expected, rtol=1e-12)
+
+    def test_gh19692_smaller_table(self):
+        # In gh-19692, we noted that the shape of the cache used in calculating
+        # p-values was dependent on the order of the inputs because the sample
+        # sizes n1 and n2 changed. This was indicative of unnecessary cache
+        # growth and redundant calculation. Check that this is resolved.
+        rng = np.random.default_rng(7600451795963068007)
+        m, n = 5, 11
+        x = rng.random(size=m)
+        y = rng.random(size=n)
+        _mwu_state.reset()  # reset cache
+        res = stats.mannwhitneyu(x, y, method='exact')
+        shape = _mwu_state.configurations.shape
+        assert shape[-1] == min(res.statistic, m*n - res.statistic) + 1
+        stats.mannwhitneyu(y, x, method='exact')
+        assert shape == _mwu_state.configurations.shape  # same when sizes are reversed
+
+        # Also, we weren't exploiting the symmmetry of the null distribution
+        # to its full potential. Ensure that the null distribution is not
+        # evaluated explicitly for `k > m*n/2`.
+        _mwu_state.reset()  # reset cache
+        stats.mannwhitneyu(x, 0*y, method='exact', alternative='greater')
+        shape = _mwu_state.configurations.shape
+        assert shape[-1] == 1  # k is smallest possible
+        stats.mannwhitneyu(0*x, y, method='exact', alternative='greater')
+        assert shape == _mwu_state.configurations.shape
+
+    @pytest.mark.parametrize('alternative', ['less', 'greater', 'two-sided'])
+    def test_permutation_method(self, alternative):
+        rng = np.random.default_rng(7600451795963068007)
+        x = rng.random(size=(2, 5))
+        y = rng.random(size=(2, 6))
+        res = stats.mannwhitneyu(x, y, method=stats.PermutationMethod(),
+                                 alternative=alternative, axis=1)
+        res2 = stats.mannwhitneyu(x, y, method='exact',
+                                  alternative=alternative, axis=1)
+        assert_allclose(res.statistic, res2.statistic, rtol=1e-15)
+        assert_allclose(res.pvalue, res2.pvalue, rtol=1e-15)
+
+
+class TestSomersD(_TestPythranFunc):
+    def setup_method(self):
+        self.dtypes = self.ALL_INTEGER + self.ALL_FLOAT
+        self.arguments = {0: (np.arange(10),
+                              self.ALL_INTEGER + self.ALL_FLOAT),
+                          1: (np.arange(10),
+                              self.ALL_INTEGER + self.ALL_FLOAT)}
+        input_array = [self.arguments[idx][0] for idx in self.arguments]
+        # In this case, self.partialfunc can simply be stats.somersd,
+        # since `alternative` is an optional argument. If it is required,
+        # we can use functools.partial to freeze the value, because
+        # we only mainly test various array inputs, not str, etc.
+        self.partialfunc = functools.partial(stats.somersd,
+                                             alternative='two-sided')
+        self.expected = self.partialfunc(*input_array)
+
+    def pythranfunc(self, *args):
+        res = self.partialfunc(*args)
+        assert_allclose(res.statistic, self.expected.statistic, atol=1e-15)
+        assert_allclose(res.pvalue, self.expected.pvalue, atol=1e-15)
+
+    def test_pythranfunc_keywords(self):
+        # Not specifying the optional keyword args
+        table = [[27, 25, 14, 7, 0], [7, 14, 18, 35, 12], [1, 3, 2, 7, 17]]
+        res1 = stats.somersd(table)
+        # Specifying the optional keyword args with default value
+        optional_args = self.get_optional_args(stats.somersd)
+        res2 = stats.somersd(table, **optional_args)
+        # Check if the results are the same in two cases
+        assert_allclose(res1.statistic, res2.statistic, atol=1e-15)
+        assert_allclose(res1.pvalue, res2.pvalue, atol=1e-15)
+
+    def test_like_kendalltau(self):
+        # All tests correspond with one in test_stats.py `test_kendalltau`
+
+        # case without ties, con-dis equal zero
+        x = [5, 2, 1, 3, 6, 4, 7, 8]
+        y = [5, 2, 6, 3, 1, 8, 7, 4]
+        # Cross-check with result from SAS FREQ:
+        expected = (0.000000000000000, 1.000000000000000)
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # case without ties, con-dis equal zero
+        x = [0, 5, 2, 1, 3, 6, 4, 7, 8]
+        y = [5, 2, 0, 6, 3, 1, 8, 7, 4]
+        # Cross-check with result from SAS FREQ:
+        expected = (0.000000000000000, 1.000000000000000)
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # case without ties, con-dis close to zero
+        x = [5, 2, 1, 3, 6, 4, 7]
+        y = [5, 2, 6, 3, 1, 7, 4]
+        # Cross-check with result from SAS FREQ:
+        expected = (-0.142857142857140, 0.630326953157670)
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # simple case without ties
+        x = np.arange(10)
+        y = np.arange(10)
+        # Cross-check with result from SAS FREQ:
+        # SAS p value is not provided.
+        expected = (1.000000000000000, 0)
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # swap a couple values and a couple more
+        x = np.arange(10)
+        y = np.array([0, 2, 1, 3, 4, 6, 5, 7, 8, 9])
+        # Cross-check with result from SAS FREQ:
+        expected = (0.911111111111110, 0.000000000000000)
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # same in opposite direction
+        x = np.arange(10)
+        y = np.arange(10)[::-1]
+        # Cross-check with result from SAS FREQ:
+        # SAS p value is not provided.
+        expected = (-1.000000000000000, 0)
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # swap a couple values and a couple more
+        x = np.arange(10)
+        y = np.array([9, 7, 8, 6, 5, 3, 4, 2, 1, 0])
+        # Cross-check with result from SAS FREQ:
+        expected = (-0.9111111111111111, 0.000000000000000)
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # with some ties
+        x1 = [12, 2, 1, 12, 2]
+        x2 = [1, 4, 7, 1, 0]
+        # Cross-check with result from SAS FREQ:
+        expected = (-0.500000000000000, 0.304901788178780)
+        res = stats.somersd(x1, x2)
+        assert_allclose(res.statistic, expected[0], atol=1e-15)
+        assert_allclose(res.pvalue, expected[1], atol=1e-15)
+
+        # with only ties in one or both inputs
+        # SAS will not produce an output for these:
+        # NOTE: No statistics are computed for x * y because x has fewer
+        # than 2 nonmissing levels.
+        # WARNING: No OUTPUT data set is produced for this table because a
+        # row or column variable has fewer than 2 nonmissing levels and no
+        # statistics are computed.
+
+        res = stats.somersd([2, 2, 2], [2, 2, 2])
+        assert_allclose(res.statistic, np.nan)
+        assert_allclose(res.pvalue, np.nan)
+
+        res = stats.somersd([2, 0, 2], [2, 2, 2])
+        assert_allclose(res.statistic, np.nan)
+        assert_allclose(res.pvalue, np.nan)
+
+        res = stats.somersd([2, 2, 2], [2, 0, 2])
+        assert_allclose(res.statistic, np.nan)
+        assert_allclose(res.pvalue, np.nan)
+
+        res = stats.somersd([0], [0])
+        assert_allclose(res.statistic, np.nan)
+        assert_allclose(res.pvalue, np.nan)
+
+        # empty arrays provided as input
+        res = stats.somersd([], [])
+        assert_allclose(res.statistic, np.nan)
+        assert_allclose(res.pvalue, np.nan)
+
+        # test unequal length inputs
+        x = np.arange(10.)
+        y = np.arange(20.)
+        assert_raises(ValueError, stats.somersd, x, y)
+
+    def test_asymmetry(self):
+        # test that somersd is asymmetric w.r.t. input order and that
+        # convention is as described: first input is row variable & independent
+        # data is from Wikipedia:
+        # https://en.wikipedia.org/wiki/Somers%27_D
+        # but currently that example contradicts itself - it says X is
+        # independent yet take D_XY
+
+        x = [1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 1, 2,
+             2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3]
+        y = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2,
+             2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]
+        # Cross-check with result from SAS FREQ:
+        d_cr = 0.272727272727270
+        d_rc = 0.342857142857140
+        p = 0.092891940883700  # same p-value for either direction
+        res = stats.somersd(x, y)
+        assert_allclose(res.statistic, d_cr, atol=1e-15)
+        assert_allclose(res.pvalue, p, atol=1e-4)
+        assert_equal(res.table.shape, (3, 2))
+        res = stats.somersd(y, x)
+        assert_allclose(res.statistic, d_rc, atol=1e-15)
+        assert_allclose(res.pvalue, p, atol=1e-15)
+        assert_equal(res.table.shape, (2, 3))
+
+    def test_somers_original(self):
+        # test against Somers' original paper [1]
+
+        # Table 5A
+        # Somers' convention was column IV
+        table = np.array([[8, 2], [6, 5], [3, 4], [1, 3], [2, 3]])
+        # Our convention (and that of SAS FREQ) is row IV
+        table = table.T
+        dyx = 129/340
+        assert_allclose(stats.somersd(table).statistic, dyx)
+
+        # table 7A - d_yx = 1
+        table = np.array([[25, 0], [85, 0], [0, 30]])
+        dxy, dyx = 3300/5425, 3300/3300
+        assert_allclose(stats.somersd(table).statistic, dxy)
+        assert_allclose(stats.somersd(table.T).statistic, dyx)
+
+        # table 7B - d_yx < 0
+        table = np.array([[25, 0], [0, 30], [85, 0]])
+        dyx = -1800/3300
+        assert_allclose(stats.somersd(table.T).statistic, dyx)
+
+    def test_contingency_table_with_zero_rows_cols(self):
+        # test that zero rows/cols in contingency table don't affect result
+
+        N = 100
+        shape = 4, 6
+        size = np.prod(shape)
+
+        np.random.seed(0)
+        s = stats.multinomial.rvs(N, p=np.ones(size)/size).reshape(shape)
+        res = stats.somersd(s)
+
+        s2 = np.insert(s, 2, np.zeros(shape[1]), axis=0)
+        res2 = stats.somersd(s2)
+
+        s3 = np.insert(s, 2, np.zeros(shape[0]), axis=1)
+        res3 = stats.somersd(s3)
+
+        s4 = np.insert(s2, 2, np.zeros(shape[0]+1), axis=1)
+        res4 = stats.somersd(s4)
+
+        # Cross-check with result from SAS FREQ:
+        assert_allclose(res.statistic, -0.116981132075470, atol=1e-15)
+        assert_allclose(res.statistic, res2.statistic)
+        assert_allclose(res.statistic, res3.statistic)
+        assert_allclose(res.statistic, res4.statistic)
+
+        assert_allclose(res.pvalue, 0.156376448188150, atol=1e-15)
+        assert_allclose(res.pvalue, res2.pvalue)
+        assert_allclose(res.pvalue, res3.pvalue)
+        assert_allclose(res.pvalue, res4.pvalue)
+
+    def test_invalid_contingency_tables(self):
+        N = 100
+        shape = 4, 6
+        size = np.prod(shape)
+
+        np.random.seed(0)
+        # start with a valid contingency table
+        s = stats.multinomial.rvs(N, p=np.ones(size)/size).reshape(shape)
+
+        s5 = s - 2
+        message = "All elements of the contingency table must be non-negative"
+        with assert_raises(ValueError, match=message):
+            stats.somersd(s5)
+
+        s6 = s + 0.01
+        message = "All elements of the contingency table must be integer"
+        with assert_raises(ValueError, match=message):
+            stats.somersd(s6)
+
+        message = ("At least two elements of the contingency "
+                   "table must be nonzero.")
+        with assert_raises(ValueError, match=message):
+            stats.somersd([[]])
+
+        with assert_raises(ValueError, match=message):
+            stats.somersd([[1]])
+
+        s7 = np.zeros((3, 3))
+        with assert_raises(ValueError, match=message):
+            stats.somersd(s7)
+
+        s7[0, 1] = 1
+        with assert_raises(ValueError, match=message):
+            stats.somersd(s7)
+
+    def test_only_ranks_matter(self):
+        # only ranks of input data should matter
+        x = [1, 2, 3]
+        x2 = [-1, 2.1, np.inf]
+        y = [3, 2, 1]
+        y2 = [0, -0.5, -np.inf]
+        res = stats.somersd(x, y)
+        res2 = stats.somersd(x2, y2)
+        assert_equal(res.statistic, res2.statistic)
+        assert_equal(res.pvalue, res2.pvalue)
+
+    def test_contingency_table_return(self):
+        # check that contingency table is returned
+        x = np.arange(10)
+        y = np.arange(10)
+        res = stats.somersd(x, y)
+        assert_equal(res.table, np.eye(10))
+
+    def test_somersd_alternative(self):
+        # Test alternative parameter, asymptotic method (due to tie)
+
+        # Based on scipy.stats.test_stats.TestCorrSpearman2::test_alternative
+        x1 = [1, 2, 3, 4, 5]
+        x2 = [5, 6, 7, 8, 7]
+
+        # strong positive correlation
+        expected = stats.somersd(x1, x2, alternative="two-sided")
+        assert expected.statistic > 0
+
+        # rank correlation > 0 -> large "less" p-value
+        res = stats.somersd(x1, x2, alternative="less")
+        assert_equal(res.statistic, expected.statistic)
+        assert_allclose(res.pvalue, 1 - (expected.pvalue / 2))
+
+        # rank correlation > 0 -> small "greater" p-value
+        res = stats.somersd(x1, x2, alternative="greater")
+        assert_equal(res.statistic, expected.statistic)
+        assert_allclose(res.pvalue, expected.pvalue / 2)
+
+        # reverse the direction of rank correlation
+        x2.reverse()
+
+        # strong negative correlation
+        expected = stats.somersd(x1, x2, alternative="two-sided")
+        assert expected.statistic < 0
+
+        # rank correlation < 0 -> large "greater" p-value
+        res = stats.somersd(x1, x2, alternative="greater")
+        assert_equal(res.statistic, expected.statistic)
+        assert_allclose(res.pvalue, 1 - (expected.pvalue / 2))
+
+        # rank correlation < 0 -> small "less" p-value
+        res = stats.somersd(x1, x2, alternative="less")
+        assert_equal(res.statistic, expected.statistic)
+        assert_allclose(res.pvalue, expected.pvalue / 2)
+
+        with pytest.raises(ValueError, match="`alternative` must be..."):
+            stats.somersd(x1, x2, alternative="ekki-ekki")
+
+    @pytest.mark.parametrize("positive_correlation", (False, True))
+    def test_somersd_perfect_correlation(self, positive_correlation):
+        # Before the addition of `alternative`, perfect correlation was
+        # treated as a special case. Now it is treated like any other case, but
+        # make sure there are no divide by zero warnings or associated errors
+
+        x1 = np.arange(10)
+        x2 = x1 if positive_correlation else np.flip(x1)
+        expected_statistic = 1 if positive_correlation else -1
+
+        # perfect correlation -> small "two-sided" p-value (0)
+        res = stats.somersd(x1, x2, alternative="two-sided")
+        assert res.statistic == expected_statistic
+        assert res.pvalue == 0
+
+        # rank correlation > 0 -> large "less" p-value (1)
+        res = stats.somersd(x1, x2, alternative="less")
+        assert res.statistic == expected_statistic
+        assert res.pvalue == (1 if positive_correlation else 0)
+
+        # rank correlation > 0 -> small "greater" p-value (0)
+        res = stats.somersd(x1, x2, alternative="greater")
+        assert res.statistic == expected_statistic
+        assert res.pvalue == (0 if positive_correlation else 1)
+
+    def test_somersd_large_inputs_gh18132(self):
+        # Test that large inputs where potential overflows could occur give
+        # the expected output. This is tested in the case of binary inputs.
+        # See gh-18126.
+
+        # generate lists of random classes 1-2 (binary)
+        classes = [1, 2]
+        n_samples = 10 ** 6
+        random.seed(6272161)
+        x = random.choices(classes, k=n_samples)
+        y = random.choices(classes, k=n_samples)
+
+        # get value to compare with: sklearn output
+        # from sklearn import metrics
+        # val_auc_sklearn = metrics.roc_auc_score(x, y)
+        # # convert to the Gini coefficient (Gini = (AUC*2)-1)
+        # val_sklearn = 2 * val_auc_sklearn - 1
+        val_sklearn = -0.001528138777036947
+
+        # calculate the Somers' D statistic, which should be equal to the
+        # result of val_sklearn until approximately machine precision
+        val_scipy = stats.somersd(x, y).statistic
+        assert_allclose(val_sklearn, val_scipy, atol=1e-15)
+
+
+class TestBarnardExact:
+    """Some tests to show that barnard_exact() works correctly."""
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[43, 40], [10, 39]], (3.555406779643, 0.000362832367)),
+            ([[100, 2], [1000, 5]], (-1.776382925679, 0.135126970878)),
+            ([[2, 7], [8, 2]], (-2.518474945157, 0.019210815430)),
+            ([[5, 1], [10, 10]], (1.449486150679, 0.156277546306)),
+            ([[5, 15], [20, 20]], (-1.851640199545, 0.066363501421)),
+            ([[5, 16], [20, 25]], (-1.609639949352, 0.116984852192)),
+            ([[10, 5], [10, 1]], (-1.449486150679, 0.177536588915)),
+            ([[5, 0], [1, 4]], (2.581988897472, 0.013671875000)),
+            ([[0, 1], [3, 2]], (-1.095445115010, 0.509667991877)),
+            ([[0, 2], [6, 4]], (-1.549193338483, 0.197019618792)),
+            ([[2, 7], [8, 2]], (-2.518474945157, 0.019210815430)),
+        ],
+    )
+    def test_precise(self, input_sample, expected):
+        """The expected values have been generated by R, using a resolution
+        for the nuisance parameter of 1e-6 :
+        ```R
+        library(Barnard)
+        options(digits=10)
+        barnard.test(43, 40, 10, 39, dp=1e-6, pooled=TRUE)
+        ```
+        """
+        res = barnard_exact(input_sample)
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_allclose([statistic, pvalue], expected)
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[43, 40], [10, 39]], (3.920362887717, 0.000289470662)),
+            ([[100, 2], [1000, 5]], (-1.139432816087, 0.950272080594)),
+            ([[2, 7], [8, 2]], (-3.079373904042, 0.020172119141)),
+            ([[5, 1], [10, 10]], (1.622375939458, 0.150599922226)),
+            ([[5, 15], [20, 20]], (-1.974771239528, 0.063038448651)),
+            ([[5, 16], [20, 25]], (-1.722122973346, 0.133329494287)),
+            ([[10, 5], [10, 1]], (-1.765469659009, 0.250566655215)),
+            ([[5, 0], [1, 4]], (5.477225575052, 0.007812500000)),
+            ([[0, 1], [3, 2]], (-1.224744871392, 0.509667991877)),
+            ([[0, 2], [6, 4]], (-1.732050807569, 0.197019618792)),
+            ([[2, 7], [8, 2]], (-3.079373904042, 0.020172119141)),
+        ],
+    )
+    def test_pooled_param(self, input_sample, expected):
+        """The expected values have been generated by R, using a resolution
+        for the nuisance parameter of 1e-6 :
+        ```R
+        library(Barnard)
+        options(digits=10)
+        barnard.test(43, 40, 10, 39, dp=1e-6, pooled=FALSE)
+        ```
+        """
+        res = barnard_exact(input_sample, pooled=False)
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_allclose([statistic, pvalue], expected)
+
+    def test_raises(self):
+        # test we raise an error for wrong input number of nuisances.
+        error_msg = (
+            "Number of points `n` must be strictly positive, found 0"
+        )
+        with assert_raises(ValueError, match=error_msg):
+            barnard_exact([[1, 2], [3, 4]], n=0)
+
+        # test we raise an error for wrong shape of input.
+        error_msg = "The input `table` must be of shape \\(2, 2\\)."
+        with assert_raises(ValueError, match=error_msg):
+            barnard_exact(np.arange(6).reshape(2, 3))
+
+        # Test all values must be positives
+        error_msg = "All values in `table` must be nonnegative."
+        with assert_raises(ValueError, match=error_msg):
+            barnard_exact([[-1, 2], [3, 4]])
+
+        # Test value error on wrong alternative param
+        error_msg = (
+            "`alternative` should be one of {'two-sided', 'less', 'greater'},"
+            " found .*"
+        )
+        with assert_raises(ValueError, match=error_msg):
+            barnard_exact([[1, 2], [3, 4]], "not-correct")
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[0, 0], [4, 3]], (1.0, 0)),
+        ],
+    )
+    def test_edge_cases(self, input_sample, expected):
+        res = barnard_exact(input_sample)
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_equal(pvalue, expected[0])
+        assert_equal(statistic, expected[1])
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[0, 5], [0, 10]], (1.0, np.nan)),
+            ([[5, 0], [10, 0]], (1.0, np.nan)),
+        ],
+    )
+    def test_row_or_col_zero(self, input_sample, expected):
+        res = barnard_exact(input_sample)
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_equal(pvalue, expected[0])
+        assert_equal(statistic, expected[1])
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[2, 7], [8, 2]], (-2.518474945157, 0.009886140845)),
+            ([[7, 200], [300, 8]], (-21.320036698460, 0.0)),
+            ([[21, 28], [1957, 6]], (-30.489638143953, 0.0)),
+        ],
+    )
+    @pytest.mark.parametrize("alternative", ["greater", "less"])
+    def test_less_greater(self, input_sample, expected, alternative):
+        """
+        "The expected values have been generated by R, using a resolution
+        for the nuisance parameter of 1e-6 :
+        ```R
+        library(Barnard)
+        options(digits=10)
+        a = barnard.test(2, 7, 8, 2, dp=1e-6, pooled=TRUE)
+        a$p.value[1]
+        ```
+        In this test, we are using the "one-sided" return value `a$p.value[1]`
+        to test our pvalue.
+        """
+        expected_stat, less_pvalue_expect = expected
+
+        if alternative == "greater":
+            input_sample = np.array(input_sample)[:, ::-1]
+            expected_stat = -expected_stat
+
+        res = barnard_exact(input_sample, alternative=alternative)
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_allclose(
+            [statistic, pvalue], [expected_stat, less_pvalue_expect], atol=1e-7
+        )
+
+
+class TestBoschlooExact:
+    """Some tests to show that boschloo_exact() works correctly."""
+
+    ATOL = 1e-7
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[2, 7], [8, 2]], (0.01852173, 0.009886142)),
+            ([[5, 1], [10, 10]], (0.9782609, 0.9450994)),
+            ([[5, 16], [20, 25]], (0.08913823, 0.05827348)),
+            ([[10, 5], [10, 1]], (0.1652174, 0.08565611)),
+            ([[5, 0], [1, 4]], (1, 1)),
+            ([[0, 1], [3, 2]], (0.5, 0.34375)),
+            ([[2, 7], [8, 2]], (0.01852173, 0.009886142)),
+            ([[7, 12], [8, 3]], (0.06406797, 0.03410916)),
+            ([[10, 24], [25, 37]], (0.2009359, 0.1512882)),
+        ],
+    )
+    def test_less(self, input_sample, expected):
+        """The expected values have been generated by R, using a resolution
+        for the nuisance parameter of 1e-8 :
+        ```R
+        library(Exact)
+        options(digits=10)
+        data <- matrix(c(43, 10, 40, 39), 2, 2, byrow=TRUE)
+        a = exact.test(data, method="Boschloo", alternative="less",
+                       tsmethod="central", np.interval=TRUE, beta=1e-8)
+        ```
+        """
+        res = boschloo_exact(input_sample, alternative="less")
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_allclose([statistic, pvalue], expected, atol=self.ATOL)
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[43, 40], [10, 39]], (0.0002875544, 0.0001615562)),
+            ([[2, 7], [8, 2]], (0.9990149, 0.9918327)),
+            ([[5, 1], [10, 10]], (0.1652174, 0.09008534)),
+            ([[5, 15], [20, 20]], (0.9849087, 0.9706997)),
+            ([[5, 16], [20, 25]], (0.972349, 0.9524124)),
+            ([[5, 0], [1, 4]], (0.02380952, 0.006865367)),
+            ([[0, 1], [3, 2]], (1, 1)),
+            ([[0, 2], [6, 4]], (1, 1)),
+            ([[2, 7], [8, 2]], (0.9990149, 0.9918327)),
+            ([[7, 12], [8, 3]], (0.9895302, 0.9771215)),
+            ([[10, 24], [25, 37]], (0.9012936, 0.8633275)),
+        ],
+    )
+    def test_greater(self, input_sample, expected):
+        """The expected values have been generated by R, using a resolution
+        for the nuisance parameter of 1e-8 :
+        ```R
+        library(Exact)
+        options(digits=10)
+        data <- matrix(c(43, 10, 40, 39), 2, 2, byrow=TRUE)
+        a = exact.test(data, method="Boschloo", alternative="greater",
+                       tsmethod="central", np.interval=TRUE, beta=1e-8)
+        ```
+        """
+        res = boschloo_exact(input_sample, alternative="greater")
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_allclose([statistic, pvalue], expected, atol=self.ATOL)
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[43, 40], [10, 39]], (0.0002875544, 0.0003231115)),
+            ([[2, 7], [8, 2]], (0.01852173, 0.01977228)),
+            ([[5, 1], [10, 10]], (0.1652174, 0.1801707)),
+            ([[5, 16], [20, 25]], (0.08913823, 0.116547)),
+            ([[5, 0], [1, 4]], (0.02380952, 0.01373073)),
+            ([[0, 1], [3, 2]], (0.5, 0.6875)),
+            ([[2, 7], [8, 2]], (0.01852173, 0.01977228)),
+            ([[7, 12], [8, 3]], (0.06406797, 0.06821831)),
+        ],
+    )
+    def test_two_sided(self, input_sample, expected):
+        """The expected values have been generated by R, using a resolution
+        for the nuisance parameter of 1e-8 :
+        ```R
+        library(Exact)
+        options(digits=10)
+        data <- matrix(c(43, 10, 40, 39), 2, 2, byrow=TRUE)
+        a = exact.test(data, method="Boschloo", alternative="two.sided",
+                       tsmethod="central", np.interval=TRUE, beta=1e-8)
+        ```
+        """
+        res = boschloo_exact(input_sample, alternative="two-sided", n=64)
+        # Need n = 64 for python 32-bit
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_allclose([statistic, pvalue], expected, atol=self.ATOL)
+
+    def test_raises(self):
+        # test we raise an error for wrong input number of nuisances.
+        error_msg = (
+            "Number of points `n` must be strictly positive, found 0"
+        )
+        with assert_raises(ValueError, match=error_msg):
+            boschloo_exact([[1, 2], [3, 4]], n=0)
+
+        # test we raise an error for wrong shape of input.
+        error_msg = "The input `table` must be of shape \\(2, 2\\)."
+        with assert_raises(ValueError, match=error_msg):
+            boschloo_exact(np.arange(6).reshape(2, 3))
+
+        # Test all values must be positives
+        error_msg = "All values in `table` must be nonnegative."
+        with assert_raises(ValueError, match=error_msg):
+            boschloo_exact([[-1, 2], [3, 4]])
+
+        # Test value error on wrong alternative param
+        error_msg = (
+            r"`alternative` should be one of \('two-sided', 'less', "
+            r"'greater'\), found .*"
+        )
+        with assert_raises(ValueError, match=error_msg):
+            boschloo_exact([[1, 2], [3, 4]], "not-correct")
+
+    @pytest.mark.parametrize(
+        "input_sample,expected",
+        [
+            ([[0, 5], [0, 10]], (np.nan, np.nan)),
+            ([[5, 0], [10, 0]], (np.nan, np.nan)),
+        ],
+    )
+    def test_row_or_col_zero(self, input_sample, expected):
+        res = boschloo_exact(input_sample)
+        statistic, pvalue = res.statistic, res.pvalue
+        assert_equal(pvalue, expected[0])
+        assert_equal(statistic, expected[1])
+
+    def test_two_sided_gt_1(self):
+        # Check that returned p-value does not exceed 1 even when twice
+        # the minimum of the one-sided p-values does. See gh-15345.
+        tbl = [[1, 1], [13, 12]]
+        pl = boschloo_exact(tbl, alternative='less').pvalue
+        pg = boschloo_exact(tbl, alternative='greater').pvalue
+        assert 2*min(pl, pg) > 1
+        pt = boschloo_exact(tbl, alternative='two-sided').pvalue
+        assert pt == 1.0
+
+    @pytest.mark.parametrize("alternative", ("less", "greater"))
+    def test_against_fisher_exact(self, alternative):
+        # Check that the statistic of `boschloo_exact` is the same as the
+        # p-value of `fisher_exact` (for one-sided tests). See gh-15345.
+        tbl = [[2, 7], [8, 2]]
+        boschloo_stat = boschloo_exact(tbl, alternative=alternative).statistic
+        fisher_p = stats.fisher_exact(tbl, alternative=alternative)[1]
+        assert_allclose(boschloo_stat, fisher_p)
+
+
+class TestCvm_2samp:
+    @pytest.mark.parametrize('args', [([], np.arange(5)),
+                                      (np.arange(5), [1])])
+    def test_too_small_input(self, args):
+        with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+            res = cramervonmises_2samp(*args)
+            assert_equal(res.statistic, np.nan)
+            assert_equal(res.pvalue, np.nan)
+
+    def test_invalid_input(self):
+        y = np.arange(5)
+        msg = 'method must be either auto, exact or asymptotic'
+        with pytest.raises(ValueError, match=msg):
+            cramervonmises_2samp(y, y, 'xyz')
+
+    def test_list_input(self):
+        x = [2, 3, 4, 7, 6]
+        y = [0.2, 0.7, 12, 18]
+        r1 = cramervonmises_2samp(x, y)
+        r2 = cramervonmises_2samp(np.array(x), np.array(y))
+        assert_equal((r1.statistic, r1.pvalue), (r2.statistic, r2.pvalue))
+
+    def test_example_conover(self):
+        # Example 2 in Section 6.2 of W.J. Conover: Practical Nonparametric
+        # Statistics, 1971.
+        x = [7.6, 8.4, 8.6, 8.7, 9.3, 9.9, 10.1, 10.6, 11.2]
+        y = [5.2, 5.7, 5.9, 6.5, 6.8, 8.2, 9.1, 9.8, 10.8, 11.3, 11.5, 12.3,
+             12.5, 13.4, 14.6]
+        r = cramervonmises_2samp(x, y)
+        assert_allclose(r.statistic, 0.262, atol=1e-3)
+        assert_allclose(r.pvalue, 0.18, atol=1e-2)
+
+    @pytest.mark.parametrize('statistic, m, n, pval',
+                             [(710, 5, 6, 48./462),
+                              (1897, 7, 7, 117./1716),
+                              (576, 4, 6, 2./210),
+                              (1764, 6, 7, 2./1716)])
+    def test_exact_pvalue(self, statistic, m, n, pval):
+        # the exact values are taken from Anderson: On the distribution of the
+        # two-sample Cramer-von-Mises criterion, 1962.
+        # The values are taken from Table 2, 3, 4 and 5
+        assert_equal(_pval_cvm_2samp_exact(statistic, m, n), pval)
+
+    @pytest.mark.xslow
+    def test_large_sample(self):
+        # for large samples, the statistic U gets very large
+        # do a sanity check that p-value is not 0, 1 or nan
+        np.random.seed(4367)
+        x = distributions.norm.rvs(size=1000000)
+        y = distributions.norm.rvs(size=900000)
+        r = cramervonmises_2samp(x, y)
+        assert_(0 < r.pvalue < 1)
+        r = cramervonmises_2samp(x, y+0.1)
+        assert_(0 < r.pvalue < 1)
+
+    def test_exact_vs_asymptotic(self):
+        np.random.seed(0)
+        x = np.random.rand(7)
+        y = np.random.rand(8)
+        r1 = cramervonmises_2samp(x, y, method='exact')
+        r2 = cramervonmises_2samp(x, y, method='asymptotic')
+        assert_equal(r1.statistic, r2.statistic)
+        assert_allclose(r1.pvalue, r2.pvalue, atol=1e-2)
+
+    def test_method_auto(self):
+        x = np.arange(20)
+        y = [0.5, 4.7, 13.1]
+        r1 = cramervonmises_2samp(x, y, method='exact')
+        r2 = cramervonmises_2samp(x, y, method='auto')
+        assert_equal(r1.pvalue, r2.pvalue)
+        # switch to asymptotic if one sample has more than 20 observations
+        x = np.arange(21)
+        r1 = cramervonmises_2samp(x, y, method='asymptotic')
+        r2 = cramervonmises_2samp(x, y, method='auto')
+        assert_equal(r1.pvalue, r2.pvalue)
+
+    def test_same_input(self):
+        # make sure trivial edge case can be handled
+        # note that _cdf_cvm_inf(0) = nan. implementation avoids nan by
+        # returning pvalue=1 for very small values of the statistic
+        x = np.arange(15)
+        res = cramervonmises_2samp(x, x)
+        assert_equal((res.statistic, res.pvalue), (0.0, 1.0))
+        # check exact p-value
+        res = cramervonmises_2samp(x[:4], x[:4])
+        assert_equal((res.statistic, res.pvalue), (0.0, 1.0))
+
+
+class TestTukeyHSD:
+
+    data_same_size = ([24.5, 23.5, 26.4, 27.1, 29.9],
+                      [28.4, 34.2, 29.5, 32.2, 30.1],
+                      [26.1, 28.3, 24.3, 26.2, 27.8])
+    data_diff_size = ([24.5, 23.5, 26.28, 26.4, 27.1, 29.9, 30.1, 30.1],
+                      [28.4, 34.2, 29.5, 32.2, 30.1],
+                      [26.1, 28.3, 24.3, 26.2, 27.8])
+    extreme_size = ([24.5, 23.5, 26.4],
+                    [28.4, 34.2, 29.5, 32.2, 30.1, 28.4, 34.2, 29.5, 32.2,
+                     30.1],
+                    [26.1, 28.3, 24.3, 26.2, 27.8])
+
+    sas_same_size = """
+    Comparison LowerCL Difference UpperCL Significance
+    2 - 3	0.6908830568	4.34	7.989116943	    1
+    2 - 1	0.9508830568	4.6 	8.249116943 	1
+    3 - 2	-7.989116943	-4.34	-0.6908830568	1
+    3 - 1	-3.389116943	0.26	3.909116943	    0
+    1 - 2	-8.249116943	-4.6	-0.9508830568	1
+    1 - 3	-3.909116943	-0.26	3.389116943	    0
+    """
+
+    sas_diff_size = """
+    Comparison LowerCL Difference UpperCL Significance
+    2 - 1	0.2679292645	3.645	7.022070736	    1
+    2 - 3	0.5934764007	4.34	8.086523599	    1
+    1 - 2	-7.022070736	-3.645	-0.2679292645	1
+    1 - 3	-2.682070736	0.695	4.072070736	    0
+    3 - 2	-8.086523599	-4.34	-0.5934764007	1
+    3 - 1	-4.072070736	-0.695	2.682070736	    0
+    """
+
+    sas_extreme = """
+    Comparison LowerCL Difference UpperCL Significance
+    2 - 3	1.561605075	    4.34	7.118394925	    1
+    2 - 1	2.740784879	    6.08	9.419215121	    1
+    3 - 2	-7.118394925	-4.34	-1.561605075	1
+    3 - 1	-1.964526566	1.74	5.444526566	    0
+    1 - 2	-9.419215121	-6.08	-2.740784879	1
+    1 - 3	-5.444526566	-1.74	1.964526566	    0
+    """
+
+    @pytest.mark.parametrize("data,res_expect_str,atol",
+                             ((data_same_size, sas_same_size, 1e-4),
+                              (data_diff_size, sas_diff_size, 1e-4),
+                              (extreme_size, sas_extreme, 1e-10),
+                              ),
+                             ids=["equal size sample",
+                                  "unequal sample size",
+                                  "extreme sample size differences"])
+    def test_compare_sas(self, data, res_expect_str, atol):
+        '''
+        SAS code used to generate results for each sample:
+        DATA ACHE;
+        INPUT BRAND RELIEF;
+        CARDS;
+        1 24.5
+        ...
+        3 27.8
+        ;
+        ods graphics on;   ODS RTF;ODS LISTING CLOSE;
+           PROC ANOVA DATA=ACHE;
+           CLASS BRAND;
+           MODEL RELIEF=BRAND;
+           MEANS BRAND/TUKEY CLDIFF;
+           TITLE 'COMPARE RELIEF ACROSS MEDICINES  - ANOVA EXAMPLE';
+           ods output  CLDiffs =tc;
+        proc print data=tc;
+            format LowerCL 17.16 UpperCL 17.16 Difference 17.16;
+            title "Output with many digits";
+        RUN;
+        QUIT;
+        ODS RTF close;
+        ODS LISTING;
+        '''
+        res_expect = np.asarray(res_expect_str.replace(" - ", " ").split()[5:],
+                                dtype=float).reshape((6, 6))
+        res_tukey = stats.tukey_hsd(*data)
+        conf = res_tukey.confidence_interval()
+        # loop over the comparisons
+        for i, j, l, s, h, sig in res_expect:
+            i, j = int(i) - 1, int(j) - 1
+            assert_allclose(conf.low[i, j], l, atol=atol)
+            assert_allclose(res_tukey.statistic[i, j], s, atol=atol)
+            assert_allclose(conf.high[i, j], h, atol=atol)
+            assert_allclose((res_tukey.pvalue[i, j] <= .05), sig == 1)
+
+    matlab_sm_siz = """
+        1	2	-8.2491590248597	-4.6	-0.9508409751403	0.0144483269098
+        1	3	-3.9091590248597	-0.26	3.3891590248597	0.9803107240900
+        2	3	0.6908409751403	4.34	7.9891590248597	0.0203311368795
+        """
+
+    matlab_diff_sz = """
+        1	2	-7.02207069748501	-3.645	-0.26792930251500 0.03371498443080
+        1	3	-2.68207069748500	0.695	4.07207069748500 0.85572267328807
+        2	3	0.59347644287720	4.34	8.08652355712281 0.02259047020620
+        """
+
+    @pytest.mark.parametrize("data,res_expect_str,atol",
+                             ((data_same_size, matlab_sm_siz, 1e-12),
+                              (data_diff_size, matlab_diff_sz, 1e-7)),
+                             ids=["equal size sample",
+                                  "unequal size sample"])
+    def test_compare_matlab(self, data, res_expect_str, atol):
+        """
+        vals = [24.5, 23.5,  26.4, 27.1, 29.9, 28.4, 34.2, 29.5, 32.2, 30.1,
+         26.1, 28.3, 24.3, 26.2, 27.8]
+        names = {'zero', 'zero', 'zero', 'zero', 'zero', 'one', 'one', 'one',
+         'one', 'one', 'two', 'two', 'two', 'two', 'two'}
+        [p,t,stats] = anova1(vals,names,"off");
+        [c,m,h,nms] = multcompare(stats, "CType","hsd");
+        """
+        res_expect = np.asarray(res_expect_str.split(),
+                                dtype=float).reshape((3, 6))
+        res_tukey = stats.tukey_hsd(*data)
+        conf = res_tukey.confidence_interval()
+        # loop over the comparisons
+        for i, j, l, s, h, p in res_expect:
+            i, j = int(i) - 1, int(j) - 1
+            assert_allclose(conf.low[i, j], l, atol=atol)
+            assert_allclose(res_tukey.statistic[i, j], s, atol=atol)
+            assert_allclose(conf.high[i, j], h, atol=atol)
+            assert_allclose(res_tukey.pvalue[i, j], p, atol=atol)
+
+    def test_compare_r(self):
+        """
+        Testing against results and p-values from R:
+        from: https://www.rdocumentation.org/packages/stats/versions/3.6.2/
+        topics/TukeyHSD
+        > require(graphics)
+        > summary(fm1 <- aov(breaks ~ tension, data = warpbreaks))
+        > TukeyHSD(fm1, "tension", ordered = TRUE)
+        > plot(TukeyHSD(fm1, "tension"))
+        Tukey multiple comparisons of means
+        95% family-wise confidence level
+        factor levels have been ordered
+        Fit: aov(formula = breaks ~ tension, data = warpbreaks)
+        $tension
+        """
+        str_res = """
+                diff        lwr      upr     p adj
+        2 - 3  4.722222 -4.8376022 14.28205 0.4630831
+        1 - 3 14.722222  5.1623978 24.28205 0.0014315
+        1 - 2 10.000000  0.4401756 19.55982 0.0384598
+        """
+        res_expect = np.asarray(str_res.replace(" - ", " ").split()[5:],
+                                dtype=float).reshape((3, 6))
+        data = ([26, 30, 54, 25, 70, 52, 51, 26, 67,
+                 27, 14, 29, 19, 29, 31, 41, 20, 44],
+                [18, 21, 29, 17, 12, 18, 35, 30, 36,
+                 42, 26, 19, 16, 39, 28, 21, 39, 29],
+                [36, 21, 24, 18, 10, 43, 28, 15, 26,
+                 20, 21, 24, 17, 13, 15, 15, 16, 28])
+
+        res_tukey = stats.tukey_hsd(*data)
+        conf = res_tukey.confidence_interval()
+        # loop over the comparisons
+        for i, j, s, l, h, p in res_expect:
+            i, j = int(i) - 1, int(j) - 1
+            # atols are set to the number of digits present in the r result.
+            assert_allclose(conf.low[i, j], l, atol=1e-7)
+            assert_allclose(res_tukey.statistic[i, j], s, atol=1e-6)
+            assert_allclose(conf.high[i, j], h, atol=1e-5)
+            assert_allclose(res_tukey.pvalue[i, j], p, atol=1e-7)
+
+    def test_engineering_stat_handbook(self):
+        '''
+        Example sourced from:
+        https://www.itl.nist.gov/div898/handbook/prc/section4/prc471.htm
+        '''
+        group1 = [6.9, 5.4, 5.8, 4.6, 4.0]
+        group2 = [8.3, 6.8, 7.8, 9.2, 6.5]
+        group3 = [8.0, 10.5, 8.1, 6.9, 9.3]
+        group4 = [5.8, 3.8, 6.1, 5.6, 6.2]
+        res = stats.tukey_hsd(group1, group2, group3, group4)
+        conf = res.confidence_interval()
+        lower = np.asarray([
+            [0, 0, 0, -2.25],
+            [.29, 0, -2.93, .13],
+            [1.13, 0, 0, .97],
+            [0, 0, 0, 0]])
+        upper = np.asarray([
+            [0, 0, 0, 1.93],
+            [4.47, 0, 1.25, 4.31],
+            [5.31, 0, 0, 5.15],
+            [0, 0, 0, 0]])
+
+        for (i, j) in [(1, 0), (2, 0), (0, 3), (1, 2), (2, 3)]:
+            assert_allclose(conf.low[i, j], lower[i, j], atol=1e-2)
+            assert_allclose(conf.high[i, j], upper[i, j], atol=1e-2)
+
+    def test_rand_symm(self):
+        # test some expected identities of the results
+        np.random.seed(1234)
+        data = np.random.rand(3, 100)
+        res = stats.tukey_hsd(*data)
+        conf = res.confidence_interval()
+        # the confidence intervals should be negated symmetric of each other
+        assert_equal(conf.low, -conf.high.T)
+        # the `high` and `low` center diagonals should be the same since the
+        # mean difference in a self comparison is 0.
+        assert_equal(np.diagonal(conf.high), conf.high[0, 0])
+        assert_equal(np.diagonal(conf.low), conf.low[0, 0])
+        # statistic array should be antisymmetric with zeros on the diagonal
+        assert_equal(res.statistic, -res.statistic.T)
+        assert_equal(np.diagonal(res.statistic), 0)
+        # p-values should be symmetric and 1 when compared to itself
+        assert_equal(res.pvalue, res.pvalue.T)
+        assert_equal(np.diagonal(res.pvalue), 1)
+
+    def test_no_inf(self):
+        with assert_raises(ValueError, match="...must be finite."):
+            stats.tukey_hsd([1, 2, 3], [2, np.inf], [6, 7, 3])
+
+    def test_is_1d(self):
+        with assert_raises(ValueError, match="...must be one-dimensional"):
+            stats.tukey_hsd([[1, 2], [2, 3]], [2, 5], [5, 23, 6])
+
+    def test_no_empty(self):
+        with assert_raises(ValueError, match="...must be greater than one"):
+            stats.tukey_hsd([], [2, 5], [4, 5, 6])
+
+    @pytest.mark.parametrize("nargs", (0, 1))
+    def test_not_enough_treatments(self, nargs):
+        with assert_raises(ValueError, match="...more than 1 treatment."):
+            stats.tukey_hsd(*([[23, 7, 3]] * nargs))
+
+    @pytest.mark.parametrize("cl", [-.5, 0, 1, 2])
+    def test_conf_level_invalid(self, cl):
+        with assert_raises(ValueError, match="must be between 0 and 1"):
+            r = stats.tukey_hsd([23, 7, 3], [3, 4], [9, 4])
+            r.confidence_interval(cl)
+
+    def test_2_args_ttest(self):
+        # that with 2 treatments the `pvalue` is equal to that of `ttest_ind`
+        res_tukey = stats.tukey_hsd(*self.data_diff_size[:2])
+        res_ttest = stats.ttest_ind(*self.data_diff_size[:2])
+        assert_allclose(res_ttest.pvalue, res_tukey.pvalue[0, 1])
+        assert_allclose(res_ttest.pvalue, res_tukey.pvalue[1, 0])
+
+
+class TestPoissonMeansTest:
+    @pytest.mark.parametrize("c1, n1, c2, n2, p_expect", (
+        # example from [1], 6. Illustrative examples: Example 1
+        [0, 100, 3, 100, 0.0884],
+        [2, 100, 6, 100, 0.1749]
+    ))
+    def test_paper_examples(self, c1, n1, c2, n2, p_expect):
+        res = stats.poisson_means_test(c1, n1, c2, n2)
+        assert_allclose(res.pvalue, p_expect, atol=1e-4)
+
+    @pytest.mark.parametrize("c1, n1, c2, n2, p_expect, alt, d", (
+        # These test cases are produced by the wrapped fortran code from the
+        # original authors. Using a slightly modified version of this fortran,
+        # found here, https://github.com/nolanbconaway/poisson-etest,
+        # additional tests were created.
+        [20, 10, 20, 10, 0.9999997568929630, 'two-sided', 0],
+        [10, 10, 10, 10, 0.9999998403241203, 'two-sided', 0],
+        [50, 15, 1, 1, 0.09920321053409643, 'two-sided', .05],
+        [3, 100, 20, 300, 0.12202725450896404, 'two-sided', 0],
+        [3, 12, 4, 20, 0.40416087318539173, 'greater', 0],
+        [4, 20, 3, 100, 0.008053640402974236, 'greater', 0],
+        # publishing paper does not include a `less` alternative,
+        # so it was calculated with switched argument order and
+        # alternative="greater"
+        [4, 20, 3, 10, 0.3083216325432898, 'less', 0],
+        [1, 1, 50, 15, 0.09322998607245102, 'less', 0]
+    ))
+    def test_fortran_authors(self, c1, n1, c2, n2, p_expect, alt, d):
+        res = stats.poisson_means_test(c1, n1, c2, n2, alternative=alt, diff=d)
+        assert_allclose(res.pvalue, p_expect, atol=2e-6, rtol=1e-16)
+
+    def test_different_results(self):
+        # The implementation in Fortran is known to break down at higher
+        # counts and observations, so we expect different results. By
+        # inspection we can infer the p-value to be near one.
+        count1, count2 = 10000, 10000
+        nobs1, nobs2 = 10000, 10000
+        res = stats.poisson_means_test(count1, nobs1, count2, nobs2)
+        assert_allclose(res.pvalue, 1)
+
+    def test_less_than_zero_lambda_hat2(self):
+        # demonstrates behavior that fixes a known fault from original Fortran.
+        # p-value should clearly be near one.
+        count1, count2 = 0, 0
+        nobs1, nobs2 = 1, 1
+        res = stats.poisson_means_test(count1, nobs1, count2, nobs2)
+        assert_allclose(res.pvalue, 1)
+
+    def test_input_validation(self):
+        count1, count2 = 0, 0
+        nobs1, nobs2 = 1, 1
+
+        # test non-integral events
+        message = '`k1` and `k2` must be integers.'
+        with assert_raises(TypeError, match=message):
+            stats.poisson_means_test(.7, nobs1, count2, nobs2)
+        with assert_raises(TypeError, match=message):
+            stats.poisson_means_test(count1, nobs1, .7, nobs2)
+
+        # test negative events
+        message = '`k1` and `k2` must be greater than or equal to 0.'
+        with assert_raises(ValueError, match=message):
+            stats.poisson_means_test(-1, nobs1, count2, nobs2)
+        with assert_raises(ValueError, match=message):
+            stats.poisson_means_test(count1, nobs1, -1, nobs2)
+
+        # test negative sample size
+        message = '`n1` and `n2` must be greater than 0.'
+        with assert_raises(ValueError, match=message):
+            stats.poisson_means_test(count1, -1, count2, nobs2)
+        with assert_raises(ValueError, match=message):
+            stats.poisson_means_test(count1, nobs1, count2, -1)
+
+        # test negative difference
+        message = 'diff must be greater than or equal to 0.'
+        with assert_raises(ValueError, match=message):
+            stats.poisson_means_test(count1, nobs1, count2, nobs2, diff=-1)
+
+        # test invalid alternatvie
+        message = 'Alternative must be one of ...'
+        with assert_raises(ValueError, match=message):
+            stats.poisson_means_test(1, 2, 1, 2, alternative='error')
+
+
+class TestBWSTest:
+
+    def test_bws_input_validation(self):
+        rng = np.random.default_rng(4571775098104213308)
+
+        x, y = rng.random(size=(2, 7))
+
+        message = '`x` and `y` must be exactly one-dimensional.'
+        with pytest.raises(ValueError, match=message):
+            stats.bws_test([x, x], [y, y])
+
+        message = '`x` and `y` must not contain NaNs.'
+        with pytest.raises(ValueError, match=message):
+            stats.bws_test([np.nan], y)
+
+        message = '`x` and `y` must be of nonzero size.'
+        with pytest.raises(ValueError, match=message):
+            stats.bws_test(x, [])
+
+        message = 'alternative` must be one of...'
+        with pytest.raises(ValueError, match=message):
+            stats.bws_test(x, y, alternative='ekki-ekki')
+
+        message = 'method` must be an instance of...'
+        with pytest.raises(ValueError, match=message):
+            stats.bws_test(x, y, method=42)
+
+
+    def test_against_published_reference(self):
+        # Test against Example 2 in bws_test Reference [1], pg 9
+        # https://link.springer.com/content/pdf/10.1007/BF02762032.pdf
+        x = [1, 2, 3, 4, 6, 7, 8]
+        y = [5, 9, 10, 11, 12, 13, 14]
+        res = stats.bws_test(x, y, alternative='two-sided')
+        assert_allclose(res.statistic, 5.132, atol=1e-3)
+        assert_equal(res.pvalue, 10/3432)
+
+
+    @pytest.mark.parametrize(('alternative', 'statistic', 'pvalue'),
+                             [('two-sided', 1.7510204081633, 0.1264422777777),
+                              ('less', -1.7510204081633, 0.05754662004662),
+                              ('greater', -1.7510204081633, 0.9424533799534)])
+    def test_against_R(self, alternative, statistic, pvalue):
+        # Test against R library BWStest function bws_test
+        # library(BWStest)
+        # options(digits=16)
+        # x = c(...)
+        # y = c(...)
+        # bws_test(x, y, alternative='two.sided')
+        rng = np.random.default_rng(4571775098104213308)
+        x, y = rng.random(size=(2, 7))
+        res = stats.bws_test(x, y, alternative=alternative)
+        assert_allclose(res.statistic, statistic, rtol=1e-13)
+        assert_allclose(res.pvalue, pvalue, atol=1e-2, rtol=1e-1)
+
+    @pytest.mark.parametrize(('alternative', 'statistic', 'pvalue'),
+                             [('two-sided', 1.142629265891, 0.2903950180801),
+                              ('less', 0.99629665877411, 0.8545660222131),
+                              ('greater', 0.99629665877411, 0.1454339777869)])
+    def test_against_R_imbalanced(self, alternative, statistic, pvalue):
+        # Test against R library BWStest function bws_test
+        # library(BWStest)
+        # options(digits=16)
+        # x = c(...)
+        # y = c(...)
+        # bws_test(x, y, alternative='two.sided')
+        rng = np.random.default_rng(5429015622386364034)
+        x = rng.random(size=9)
+        y = rng.random(size=8)
+        res = stats.bws_test(x, y, alternative=alternative)
+        assert_allclose(res.statistic, statistic, rtol=1e-13)
+        assert_allclose(res.pvalue, pvalue, atol=1e-2, rtol=1e-1)
+
+    def test_method(self):
+        # Test that `method` parameter has the desired effect
+        rng = np.random.default_rng(1520514347193347862)
+        x, y = rng.random(size=(2, 10))
+
+        rng = np.random.default_rng(1520514347193347862)
+        method = stats.PermutationMethod(n_resamples=10, random_state=rng)
+        res1 = stats.bws_test(x, y, method=method)
+
+        assert len(res1.null_distribution) == 10
+
+        rng = np.random.default_rng(1520514347193347862)
+        method = stats.PermutationMethod(n_resamples=10, random_state=rng)
+        res2 = stats.bws_test(x, y, method=method)
+
+        assert_allclose(res1.null_distribution, res2.null_distribution)
+
+        rng = np.random.default_rng(5205143471933478621)
+        method = stats.PermutationMethod(n_resamples=10, random_state=rng)
+        res3 = stats.bws_test(x, y, method=method)
+
+        assert not np.allclose(res3.null_distribution, res1.null_distribution)
+
+    def test_directions(self):
+        # Sanity check of the sign of the one-sided statistic
+        rng = np.random.default_rng(1520514347193347862)
+        x = rng.random(size=5)
+        y = x - 1
+
+        res = stats.bws_test(x, y, alternative='greater')
+        assert res.statistic > 0
+        assert_equal(res.pvalue, 1 / len(res.null_distribution))
+
+        res = stats.bws_test(x, y, alternative='less')
+        assert res.statistic > 0
+        assert_equal(res.pvalue, 1)
+
+        res = stats.bws_test(y, x, alternative='less')
+        assert res.statistic < 0
+        assert_equal(res.pvalue, 1 / len(res.null_distribution))
+
+        res = stats.bws_test(y, x, alternative='greater')
+        assert res.statistic < 0
+        assert_equal(res.pvalue, 1)

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_kdeoth.py

@@ -0,0 +1,608 @@
+from scipy import stats, linalg, integrate
+import numpy as np
+from numpy.testing import (assert_almost_equal, assert_, assert_equal,
+                           assert_array_almost_equal,
+                           assert_array_almost_equal_nulp, assert_allclose)
+import pytest
+from pytest import raises as assert_raises
+
+
+def test_kde_1d():
+    #some basic tests comparing to normal distribution
+    np.random.seed(8765678)
+    n_basesample = 500
+    xn = np.random.randn(n_basesample)
+    xnmean = xn.mean()
+    xnstd = xn.std(ddof=1)
+
+    # get kde for original sample
+    gkde = stats.gaussian_kde(xn)
+
+    # evaluate the density function for the kde for some points
+    xs = np.linspace(-7,7,501)
+    kdepdf = gkde.evaluate(xs)
+    normpdf = stats.norm.pdf(xs, loc=xnmean, scale=xnstd)
+    intervall = xs[1] - xs[0]
+
+    assert_(np.sum((kdepdf - normpdf)**2)*intervall < 0.01)
+    prob1 = gkde.integrate_box_1d(xnmean, np.inf)
+    prob2 = gkde.integrate_box_1d(-np.inf, xnmean)
+    assert_almost_equal(prob1, 0.5, decimal=1)
+    assert_almost_equal(prob2, 0.5, decimal=1)
+    assert_almost_equal(gkde.integrate_box(xnmean, np.inf), prob1, decimal=13)
+    assert_almost_equal(gkde.integrate_box(-np.inf, xnmean), prob2, decimal=13)
+
+    assert_almost_equal(gkde.integrate_kde(gkde),
+                        (kdepdf**2).sum()*intervall, decimal=2)
+    assert_almost_equal(gkde.integrate_gaussian(xnmean, xnstd**2),
+                        (kdepdf*normpdf).sum()*intervall, decimal=2)
+
+
+def test_kde_1d_weighted():
+    #some basic tests comparing to normal distribution
+    np.random.seed(8765678)
+    n_basesample = 500
+    xn = np.random.randn(n_basesample)
+    wn = np.random.rand(n_basesample)
+    xnmean = np.average(xn, weights=wn)
+    xnstd = np.sqrt(np.average((xn-xnmean)**2, weights=wn))
+
+    # get kde for original sample
+    gkde = stats.gaussian_kde(xn, weights=wn)
+
+    # evaluate the density function for the kde for some points
+    xs = np.linspace(-7,7,501)
+    kdepdf = gkde.evaluate(xs)
+    normpdf = stats.norm.pdf(xs, loc=xnmean, scale=xnstd)
+    intervall = xs[1] - xs[0]
+
+    assert_(np.sum((kdepdf - normpdf)**2)*intervall < 0.01)
+    prob1 = gkde.integrate_box_1d(xnmean, np.inf)
+    prob2 = gkde.integrate_box_1d(-np.inf, xnmean)
+    assert_almost_equal(prob1, 0.5, decimal=1)
+    assert_almost_equal(prob2, 0.5, decimal=1)
+    assert_almost_equal(gkde.integrate_box(xnmean, np.inf), prob1, decimal=13)
+    assert_almost_equal(gkde.integrate_box(-np.inf, xnmean), prob2, decimal=13)
+
+    assert_almost_equal(gkde.integrate_kde(gkde),
+                        (kdepdf**2).sum()*intervall, decimal=2)
+    assert_almost_equal(gkde.integrate_gaussian(xnmean, xnstd**2),
+                        (kdepdf*normpdf).sum()*intervall, decimal=2)
+
+
+@pytest.mark.xslow
+def test_kde_2d():
+    #some basic tests comparing to normal distribution
+    np.random.seed(8765678)
+    n_basesample = 500
+
+    mean = np.array([1.0, 3.0])
+    covariance = np.array([[1.0, 2.0], [2.0, 6.0]])
+
+    # Need transpose (shape (2, 500)) for kde
+    xn = np.random.multivariate_normal(mean, covariance, size=n_basesample).T
+
+    # get kde for original sample
+    gkde = stats.gaussian_kde(xn)
+
+    # evaluate the density function for the kde for some points
+    x, y = np.mgrid[-7:7:500j, -7:7:500j]
+    grid_coords = np.vstack([x.ravel(), y.ravel()])
+    kdepdf = gkde.evaluate(grid_coords)
+    kdepdf = kdepdf.reshape(500, 500)
+
+    normpdf = stats.multivariate_normal.pdf(np.dstack([x, y]),
+                                            mean=mean, cov=covariance)
+    intervall = y.ravel()[1] - y.ravel()[0]
+
+    assert_(np.sum((kdepdf - normpdf)**2) * (intervall**2) < 0.01)
+
+    small = -1e100
+    large = 1e100
+    prob1 = gkde.integrate_box([small, mean[1]], [large, large])
+    prob2 = gkde.integrate_box([small, small], [large, mean[1]])
+
+    assert_almost_equal(prob1, 0.5, decimal=1)
+    assert_almost_equal(prob2, 0.5, decimal=1)
+    assert_almost_equal(gkde.integrate_kde(gkde),
+                        (kdepdf**2).sum()*(intervall**2), decimal=2)
+    assert_almost_equal(gkde.integrate_gaussian(mean, covariance),
+                        (kdepdf*normpdf).sum()*(intervall**2), decimal=2)
+
+
+@pytest.mark.xslow
+def test_kde_2d_weighted():
+    #some basic tests comparing to normal distribution
+    np.random.seed(8765678)
+    n_basesample = 500
+
+    mean = np.array([1.0, 3.0])
+    covariance = np.array([[1.0, 2.0], [2.0, 6.0]])
+
+    # Need transpose (shape (2, 500)) for kde
+    xn = np.random.multivariate_normal(mean, covariance, size=n_basesample).T
+    wn = np.random.rand(n_basesample)
+
+    # get kde for original sample
+    gkde = stats.gaussian_kde(xn, weights=wn)
+
+    # evaluate the density function for the kde for some points
+    x, y = np.mgrid[-7:7:500j, -7:7:500j]
+    grid_coords = np.vstack([x.ravel(), y.ravel()])
+    kdepdf = gkde.evaluate(grid_coords)
+    kdepdf = kdepdf.reshape(500, 500)
+
+    normpdf = stats.multivariate_normal.pdf(np.dstack([x, y]),
+                                            mean=mean, cov=covariance)
+    intervall = y.ravel()[1] - y.ravel()[0]
+
+    assert_(np.sum((kdepdf - normpdf)**2) * (intervall**2) < 0.01)
+
+    small = -1e100
+    large = 1e100
+    prob1 = gkde.integrate_box([small, mean[1]], [large, large])
+    prob2 = gkde.integrate_box([small, small], [large, mean[1]])
+
+    assert_almost_equal(prob1, 0.5, decimal=1)
+    assert_almost_equal(prob2, 0.5, decimal=1)
+    assert_almost_equal(gkde.integrate_kde(gkde),
+                        (kdepdf**2).sum()*(intervall**2), decimal=2)
+    assert_almost_equal(gkde.integrate_gaussian(mean, covariance),
+                        (kdepdf*normpdf).sum()*(intervall**2), decimal=2)
+
+
+def test_kde_bandwidth_method():
+    def scotts_factor(kde_obj):
+        """Same as default, just check that it works."""
+        return np.power(kde_obj.n, -1./(kde_obj.d+4))
+
+    np.random.seed(8765678)
+    n_basesample = 50
+    xn = np.random.randn(n_basesample)
+
+    # Default
+    gkde = stats.gaussian_kde(xn)
+    # Supply a callable
+    gkde2 = stats.gaussian_kde(xn, bw_method=scotts_factor)
+    # Supply a scalar
+    gkde3 = stats.gaussian_kde(xn, bw_method=gkde.factor)
+
+    xs = np.linspace(-7,7,51)
+    kdepdf = gkde.evaluate(xs)
+    kdepdf2 = gkde2.evaluate(xs)
+    assert_almost_equal(kdepdf, kdepdf2)
+    kdepdf3 = gkde3.evaluate(xs)
+    assert_almost_equal(kdepdf, kdepdf3)
+
+    assert_raises(ValueError, stats.gaussian_kde, xn, bw_method='wrongstring')
+
+
+def test_kde_bandwidth_method_weighted():
+    def scotts_factor(kde_obj):
+        """Same as default, just check that it works."""
+        return np.power(kde_obj.neff, -1./(kde_obj.d+4))
+
+    np.random.seed(8765678)
+    n_basesample = 50
+    xn = np.random.randn(n_basesample)
+
+    # Default
+    gkde = stats.gaussian_kde(xn)
+    # Supply a callable
+    gkde2 = stats.gaussian_kde(xn, bw_method=scotts_factor)
+    # Supply a scalar
+    gkde3 = stats.gaussian_kde(xn, bw_method=gkde.factor)
+
+    xs = np.linspace(-7,7,51)
+    kdepdf = gkde.evaluate(xs)
+    kdepdf2 = gkde2.evaluate(xs)
+    assert_almost_equal(kdepdf, kdepdf2)
+    kdepdf3 = gkde3.evaluate(xs)
+    assert_almost_equal(kdepdf, kdepdf3)
+
+    assert_raises(ValueError, stats.gaussian_kde, xn, bw_method='wrongstring')
+
+
+# Subclasses that should stay working (extracted from various sources).
+# Unfortunately the earlier design of gaussian_kde made it necessary for users
+# to create these kinds of subclasses, or call _compute_covariance() directly.
+
+class _kde_subclass1(stats.gaussian_kde):
+    def __init__(self, dataset):
+        self.dataset = np.atleast_2d(dataset)
+        self.d, self.n = self.dataset.shape
+        self.covariance_factor = self.scotts_factor
+        self._compute_covariance()
+
+
+class _kde_subclass2(stats.gaussian_kde):
+    def __init__(self, dataset):
+        self.covariance_factor = self.scotts_factor
+        super().__init__(dataset)
+
+
+class _kde_subclass4(stats.gaussian_kde):
+    def covariance_factor(self):
+        return 0.5 * self.silverman_factor()
+
+
+def test_gaussian_kde_subclassing():
+    x1 = np.array([-7, -5, 1, 4, 5], dtype=float)
+    xs = np.linspace(-10, 10, num=50)
+
+    # gaussian_kde itself
+    kde = stats.gaussian_kde(x1)
+    ys = kde(xs)
+
+    # subclass 1
+    kde1 = _kde_subclass1(x1)
+    y1 = kde1(xs)
+    assert_array_almost_equal_nulp(ys, y1, nulp=10)
+
+    # subclass 2
+    kde2 = _kde_subclass2(x1)
+    y2 = kde2(xs)
+    assert_array_almost_equal_nulp(ys, y2, nulp=10)
+
+    # subclass 3 was removed because we have no obligation to maintain support
+    # for user invocation of private methods
+
+    # subclass 4
+    kde4 = _kde_subclass4(x1)
+    y4 = kde4(x1)
+    y_expected = [0.06292987, 0.06346938, 0.05860291, 0.08657652, 0.07904017]
+
+    assert_array_almost_equal(y_expected, y4, decimal=6)
+
+    # Not a subclass, but check for use of _compute_covariance()
+    kde5 = kde
+    kde5.covariance_factor = lambda: kde.factor
+    kde5._compute_covariance()
+    y5 = kde5(xs)
+    assert_array_almost_equal_nulp(ys, y5, nulp=10)
+
+
+def test_gaussian_kde_covariance_caching():
+    x1 = np.array([-7, -5, 1, 4, 5], dtype=float)
+    xs = np.linspace(-10, 10, num=5)
+    # These expected values are from scipy 0.10, before some changes to
+    # gaussian_kde.  They were not compared with any external reference.
+    y_expected = [0.02463386, 0.04689208, 0.05395444, 0.05337754, 0.01664475]
+
+    # Set the bandwidth, then reset it to the default.
+    kde = stats.gaussian_kde(x1)
+    kde.set_bandwidth(bw_method=0.5)
+    kde.set_bandwidth(bw_method='scott')
+    y2 = kde(xs)
+
+    assert_array_almost_equal(y_expected, y2, decimal=7)
+
+
+def test_gaussian_kde_monkeypatch():
+    """Ugly, but people may rely on this.  See scipy pull request 123,
+    specifically the linked ML thread "Width of the Gaussian in stats.kde".
+    If it is necessary to break this later on, that is to be discussed on ML.
+    """
+    x1 = np.array([-7, -5, 1, 4, 5], dtype=float)
+    xs = np.linspace(-10, 10, num=50)
+
+    # The old monkeypatched version to get at Silverman's Rule.
+    kde = stats.gaussian_kde(x1)
+    kde.covariance_factor = kde.silverman_factor
+    kde._compute_covariance()
+    y1 = kde(xs)
+
+    # The new saner version.
+    kde2 = stats.gaussian_kde(x1, bw_method='silverman')
+    y2 = kde2(xs)
+
+    assert_array_almost_equal_nulp(y1, y2, nulp=10)
+
+
+def test_kde_integer_input():
+    """Regression test for #1181."""
+    x1 = np.arange(5)
+    kde = stats.gaussian_kde(x1)
+    y_expected = [0.13480721, 0.18222869, 0.19514935, 0.18222869, 0.13480721]
+    assert_array_almost_equal(kde(x1), y_expected, decimal=6)
+
+
+_ftypes = ['float32', 'float64', 'float96', 'float128', 'int32', 'int64']
+
+
+@pytest.mark.parametrize("bw_type", _ftypes + ["scott", "silverman"])
+@pytest.mark.parametrize("dtype", _ftypes)
+def test_kde_output_dtype(dtype, bw_type):
+    # Check whether the datatypes are available
+    dtype = getattr(np, dtype, None)
+
+    if bw_type in ["scott", "silverman"]:
+        bw = bw_type
+    else:
+        bw_type = getattr(np, bw_type, None)
+        bw = bw_type(3) if bw_type else None
+
+    if any(dt is None for dt in [dtype, bw]):
+        pytest.skip()
+
+    weights = np.arange(5, dtype=dtype)
+    dataset = np.arange(5, dtype=dtype)
+    k = stats.gaussian_kde(dataset, bw_method=bw, weights=weights)
+    points = np.arange(5, dtype=dtype)
+    result = k(points)
+    # weights are always cast to float64
+    assert result.dtype == np.result_type(dataset, points, np.float64(weights),
+                                          k.factor)
+
+
+def test_pdf_logpdf_validation():
+    rng = np.random.default_rng(64202298293133848336925499069837723291)
+    xn = rng.standard_normal((2, 10))
+    gkde = stats.gaussian_kde(xn)
+    xs = rng.standard_normal((3, 10))
+
+    msg = "points have dimension 3, dataset has dimension 2"
+    with pytest.raises(ValueError, match=msg):
+        gkde.logpdf(xs)
+
+
+def test_pdf_logpdf():
+    np.random.seed(1)
+    n_basesample = 50
+    xn = np.random.randn(n_basesample)
+
+    # Default
+    gkde = stats.gaussian_kde(xn)
+
+    xs = np.linspace(-15, 12, 25)
+    pdf = gkde.evaluate(xs)
+    pdf2 = gkde.pdf(xs)
+    assert_almost_equal(pdf, pdf2, decimal=12)
+
+    logpdf = np.log(pdf)
+    logpdf2 = gkde.logpdf(xs)
+    assert_almost_equal(logpdf, logpdf2, decimal=12)
+
+    # There are more points than data
+    gkde = stats.gaussian_kde(xs)
+    pdf = np.log(gkde.evaluate(xn))
+    pdf2 = gkde.logpdf(xn)
+    assert_almost_equal(pdf, pdf2, decimal=12)
+
+
+def test_pdf_logpdf_weighted():
+    np.random.seed(1)
+    n_basesample = 50
+    xn = np.random.randn(n_basesample)
+    wn = np.random.rand(n_basesample)
+
+    # Default
+    gkde = stats.gaussian_kde(xn, weights=wn)
+
+    xs = np.linspace(-15, 12, 25)
+    pdf = gkde.evaluate(xs)
+    pdf2 = gkde.pdf(xs)
+    assert_almost_equal(pdf, pdf2, decimal=12)
+
+    logpdf = np.log(pdf)
+    logpdf2 = gkde.logpdf(xs)
+    assert_almost_equal(logpdf, logpdf2, decimal=12)
+
+    # There are more points than data
+    gkde = stats.gaussian_kde(xs, weights=np.random.rand(len(xs)))
+    pdf = np.log(gkde.evaluate(xn))
+    pdf2 = gkde.logpdf(xn)
+    assert_almost_equal(pdf, pdf2, decimal=12)
+
+
+def test_marginal_1_axis():
+    rng = np.random.default_rng(6111799263660870475)
+    n_data = 50
+    n_dim = 10
+    dataset = rng.normal(size=(n_dim, n_data))
+    points = rng.normal(size=(n_dim, 3))
+
+    dimensions = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9])  # dimensions to keep
+
+    kde = stats.gaussian_kde(dataset)
+    marginal = kde.marginal(dimensions)
+    pdf = marginal.pdf(points[dimensions])
+
+    def marginal_pdf_single(point):
+        def f(x):
+            x = np.concatenate(([x], point[dimensions]))
+            return kde.pdf(x)[0]
+        return integrate.quad(f, -np.inf, np.inf)[0]
+
+    def marginal_pdf(points):
+        return np.apply_along_axis(marginal_pdf_single, axis=0, arr=points)
+
+    ref = marginal_pdf(points)
+
+    assert_allclose(pdf, ref, rtol=1e-6)
+
+
+@pytest.mark.xslow
+def test_marginal_2_axis():
+    rng = np.random.default_rng(6111799263660870475)
+    n_data = 30
+    n_dim = 4
+    dataset = rng.normal(size=(n_dim, n_data))
+    points = rng.normal(size=(n_dim, 3))
+
+    dimensions = np.array([1, 3])  # dimensions to keep
+
+    kde = stats.gaussian_kde(dataset)
+    marginal = kde.marginal(dimensions)
+    pdf = marginal.pdf(points[dimensions])
+
+    def marginal_pdf(points):
+        def marginal_pdf_single(point):
+            def f(y, x):
+                w, z = point[dimensions]
+                x = np.array([x, w, y, z])
+                return kde.pdf(x)[0]
+            return integrate.dblquad(f, -np.inf, np.inf, -np.inf, np.inf)[0]
+
+        return np.apply_along_axis(marginal_pdf_single, axis=0, arr=points)
+
+    ref = marginal_pdf(points)
+
+    assert_allclose(pdf, ref, rtol=1e-6)
+
+
+def test_marginal_iv():
+    # test input validation
+    rng = np.random.default_rng(6111799263660870475)
+    n_data = 30
+    n_dim = 4
+    dataset = rng.normal(size=(n_dim, n_data))
+    points = rng.normal(size=(n_dim, 3))
+
+    kde = stats.gaussian_kde(dataset)
+
+    # check that positive and negative indices are equivalent
+    dimensions1 = [-1, 1]
+    marginal1 = kde.marginal(dimensions1)
+    pdf1 = marginal1.pdf(points[dimensions1])
+
+    dimensions2 = [3, -3]
+    marginal2 = kde.marginal(dimensions2)
+    pdf2 = marginal2.pdf(points[dimensions2])
+
+    assert_equal(pdf1, pdf2)
+
+    # IV for non-integer dimensions
+    message = "Elements of `dimensions` must be integers..."
+    with pytest.raises(ValueError, match=message):
+        kde.marginal([1, 2.5])
+
+    # IV for uniquenes
+    message = "All elements of `dimensions` must be unique."
+    with pytest.raises(ValueError, match=message):
+        kde.marginal([1, 2, 2])
+
+    # IV for non-integer dimensions
+    message = (r"Dimensions \[-5  6\] are invalid for a distribution in 4...")
+    with pytest.raises(ValueError, match=message):
+        kde.marginal([1, -5, 6])
+
+
+@pytest.mark.xslow
+def test_logpdf_overflow():
+    # regression test for gh-12988; testing against linalg instability for
+    # very high dimensionality kde
+    np.random.seed(1)
+    n_dimensions = 2500
+    n_samples = 5000
+    xn = np.array([np.random.randn(n_samples) + (n) for n in range(
+        0, n_dimensions)])
+
+    # Default
+    gkde = stats.gaussian_kde(xn)
+
+    logpdf = gkde.logpdf(np.arange(0, n_dimensions))
+    np.testing.assert_equal(np.isneginf(logpdf[0]), False)
+    np.testing.assert_equal(np.isnan(logpdf[0]), False)
+
+
+def test_weights_intact():
+    # regression test for gh-9709: weights are not modified
+    np.random.seed(12345)
+    vals = np.random.lognormal(size=100)
+    weights = np.random.choice([1.0, 10.0, 100], size=vals.size)
+    orig_weights = weights.copy()
+
+    stats.gaussian_kde(np.log10(vals), weights=weights)
+    assert_allclose(weights, orig_weights, atol=1e-14, rtol=1e-14)
+
+
+def test_weights_integer():
+    # integer weights are OK, cf gh-9709 (comment)
+    np.random.seed(12345)
+    values = [0.2, 13.5, 21.0, 75.0, 99.0]
+    weights = [1, 2, 4, 8, 16]  # a list of integers
+    pdf_i = stats.gaussian_kde(values, weights=weights)
+    pdf_f = stats.gaussian_kde(values, weights=np.float64(weights))
+
+    xn = [0.3, 11, 88]
+    assert_allclose(pdf_i.evaluate(xn),
+                    pdf_f.evaluate(xn), atol=1e-14, rtol=1e-14)
+
+
+def test_seed():
+    # Test the seed option of the resample method
+    def test_seed_sub(gkde_trail):
+        n_sample = 200
+        # The results should be different without using seed
+        samp1 = gkde_trail.resample(n_sample)
+        samp2 = gkde_trail.resample(n_sample)
+        assert_raises(
+            AssertionError, assert_allclose, samp1, samp2, atol=1e-13
+        )
+        # Use integer seed
+        seed = 831
+        samp1 = gkde_trail.resample(n_sample, seed=seed)
+        samp2 = gkde_trail.resample(n_sample, seed=seed)
+        assert_allclose(samp1, samp2, atol=1e-13)
+        # Use RandomState
+        rstate1 = np.random.RandomState(seed=138)
+        samp1 = gkde_trail.resample(n_sample, seed=rstate1)
+        rstate2 = np.random.RandomState(seed=138)
+        samp2 = gkde_trail.resample(n_sample, seed=rstate2)
+        assert_allclose(samp1, samp2, atol=1e-13)
+
+        # check that np.random.Generator can be used (numpy >= 1.17)
+        if hasattr(np.random, 'default_rng'):
+            # obtain a np.random.Generator object
+            rng = np.random.default_rng(1234)
+            gkde_trail.resample(n_sample, seed=rng)
+
+    np.random.seed(8765678)
+    n_basesample = 500
+    wn = np.random.rand(n_basesample)
+    # Test 1D case
+    xn_1d = np.random.randn(n_basesample)
+
+    gkde_1d = stats.gaussian_kde(xn_1d)
+    test_seed_sub(gkde_1d)
+    gkde_1d_weighted = stats.gaussian_kde(xn_1d, weights=wn)
+    test_seed_sub(gkde_1d_weighted)
+
+    # Test 2D case
+    mean = np.array([1.0, 3.0])
+    covariance = np.array([[1.0, 2.0], [2.0, 6.0]])
+    xn_2d = np.random.multivariate_normal(mean, covariance, size=n_basesample).T
+
+    gkde_2d = stats.gaussian_kde(xn_2d)
+    test_seed_sub(gkde_2d)
+    gkde_2d_weighted = stats.gaussian_kde(xn_2d, weights=wn)
+    test_seed_sub(gkde_2d_weighted)
+
+
+def test_singular_data_covariance_gh10205():
+    # When the data lie in a lower-dimensional subspace and this causes
+    # and exception, check that the error message is informative.
+    rng = np.random.default_rng(2321583144339784787)
+    mu = np.array([1, 10, 20])
+    sigma = np.array([[4, 10, 0], [10, 25, 0], [0, 0, 100]])
+    data = rng.multivariate_normal(mu, sigma, 1000)
+    try:  # doesn't raise any error on some platforms, and that's OK
+        stats.gaussian_kde(data.T)
+    except linalg.LinAlgError:
+        msg = "The data appears to lie in a lower-dimensional subspace..."
+        with assert_raises(linalg.LinAlgError, match=msg):
+            stats.gaussian_kde(data.T)
+
+
+def test_fewer_points_than_dimensions_gh17436():
+    # When the number of points is fewer than the number of dimensions, the
+    # the covariance matrix would be singular, and the exception tested in
+    # test_singular_data_covariance_gh10205 would occur. However, sometimes
+    # this occurs when the user passes in the transpose of what `gaussian_kde`
+    # expects. This can result in a huge covariance matrix, so bail early.
+    rng = np.random.default_rng(2046127537594925772)
+    rvs = rng.multivariate_normal(np.zeros(3), np.eye(3), size=5)
+    message = "Number of dimensions is greater than number of samples..."
+    with pytest.raises(ValueError, match=message):
+        stats.gaussian_kde(rvs)

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_mgc.py

@@ -0,0 +1,217 @@
+import pytest
+from pytest import raises as assert_raises, warns as assert_warns
+
+import numpy as np
+from numpy.testing import assert_approx_equal, assert_allclose, assert_equal
+
+from scipy.spatial.distance import cdist
+from scipy import stats
+
+class TestMGCErrorWarnings:
+    """ Tests errors and warnings derived from MGC.
+    """
+    def test_error_notndarray(self):
+        # raises error if x or y is not a ndarray
+        x = np.arange(20)
+        y = [5] * 20
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, y)
+        assert_raises(ValueError, stats.multiscale_graphcorr, y, x)
+
+    def test_error_shape(self):
+        # raises error if number of samples different (n)
+        x = np.arange(100).reshape(25, 4)
+        y = x.reshape(10, 10)
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, y)
+
+    def test_error_lowsamples(self):
+        # raises error if samples are low (< 3)
+        x = np.arange(3)
+        y = np.arange(3)
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, y)
+
+    def test_error_nans(self):
+        # raises error if inputs contain NaNs
+        x = np.arange(20, dtype=float)
+        x[0] = np.nan
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, x)
+
+        y = np.arange(20)
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, y)
+
+    def test_error_wrongdisttype(self):
+        # raises error if metric is not a function
+        x = np.arange(20)
+        compute_distance = 0
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, x,
+                      compute_distance=compute_distance)
+
+    @pytest.mark.parametrize("reps", [
+        -1,    # reps is negative
+        '1',   # reps is not integer
+    ])
+    def test_error_reps(self, reps):
+        # raises error if reps is negative
+        x = np.arange(20)
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, x, reps=reps)
+
+    def test_warns_reps(self):
+        # raises warning when reps is less than 1000
+        x = np.arange(20)
+        reps = 100
+        assert_warns(RuntimeWarning, stats.multiscale_graphcorr, x, x, reps=reps)
+
+    def test_error_infty(self):
+        # raises error if input contains infinities
+        x = np.arange(20)
+        y = np.ones(20) * np.inf
+        assert_raises(ValueError, stats.multiscale_graphcorr, x, y)
+
+
+class TestMGCStat:
+    """ Test validity of MGC test statistic
+    """
+    def _simulations(self, samps=100, dims=1, sim_type=""):
+        # linear simulation
+        if sim_type == "linear":
+            x = np.random.uniform(-1, 1, size=(samps, 1))
+            y = x + 0.3 * np.random.random_sample(size=(x.size, 1))
+
+        # spiral simulation
+        elif sim_type == "nonlinear":
+            unif = np.array(np.random.uniform(0, 5, size=(samps, 1)))
+            x = unif * np.cos(np.pi * unif)
+            y = (unif * np.sin(np.pi * unif) +
+                 0.4*np.random.random_sample(size=(x.size, 1)))
+
+        # independence (tests type I simulation)
+        elif sim_type == "independence":
+            u = np.random.normal(0, 1, size=(samps, 1))
+            v = np.random.normal(0, 1, size=(samps, 1))
+            u_2 = np.random.binomial(1, p=0.5, size=(samps, 1))
+            v_2 = np.random.binomial(1, p=0.5, size=(samps, 1))
+            x = u/3 + 2*u_2 - 1
+            y = v/3 + 2*v_2 - 1
+
+        # raises error if not approved sim_type
+        else:
+            raise ValueError("sim_type must be linear, nonlinear, or "
+                             "independence")
+
+        # add dimensions of noise for higher dimensions
+        if dims > 1:
+            dims_noise = np.random.normal(0, 1, size=(samps, dims-1))
+            x = np.concatenate((x, dims_noise), axis=1)
+
+        return x, y
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize("sim_type, obs_stat, obs_pvalue", [
+        ("linear", 0.97, 1/1000),           # test linear simulation
+        ("nonlinear", 0.163, 1/1000),       # test spiral simulation
+        ("independence", -0.0094, 0.78)     # test independence simulation
+    ])
+    def test_oned(self, sim_type, obs_stat, obs_pvalue):
+        np.random.seed(12345678)
+
+        # generate x and y
+        x, y = self._simulations(samps=100, dims=1, sim_type=sim_type)
+
+        # test stat and pvalue
+        stat, pvalue, _ = stats.multiscale_graphcorr(x, y)
+        assert_approx_equal(stat, obs_stat, significant=1)
+        assert_approx_equal(pvalue, obs_pvalue, significant=1)
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize("sim_type, obs_stat, obs_pvalue", [
+        ("linear", 0.184, 1/1000),           # test linear simulation
+        ("nonlinear", 0.0190, 0.117),        # test spiral simulation
+    ])
+    def test_fived(self, sim_type, obs_stat, obs_pvalue):
+        np.random.seed(12345678)
+
+        # generate x and y
+        x, y = self._simulations(samps=100, dims=5, sim_type=sim_type)
+
+        # test stat and pvalue
+        stat, pvalue, _ = stats.multiscale_graphcorr(x, y)
+        assert_approx_equal(stat, obs_stat, significant=1)
+        assert_approx_equal(pvalue, obs_pvalue, significant=1)
+
+    @pytest.mark.xslow
+    def test_twosamp(self):
+        np.random.seed(12345678)
+
+        # generate x and y
+        x = np.random.binomial(100, 0.5, size=(100, 5))
+        y = np.random.normal(0, 1, size=(80, 5))
+
+        # test stat and pvalue
+        stat, pvalue, _ = stats.multiscale_graphcorr(x, y)
+        assert_approx_equal(stat, 1.0, significant=1)
+        assert_approx_equal(pvalue, 0.001, significant=1)
+
+        # generate x and y
+        y = np.random.normal(0, 1, size=(100, 5))
+
+        # test stat and pvalue
+        stat, pvalue, _ = stats.multiscale_graphcorr(x, y, is_twosamp=True)
+        assert_approx_equal(stat, 1.0, significant=1)
+        assert_approx_equal(pvalue, 0.001, significant=1)
+
+    @pytest.mark.xslow
+    def test_workers(self):
+        np.random.seed(12345678)
+
+        # generate x and y
+        x, y = self._simulations(samps=100, dims=1, sim_type="linear")
+
+        # test stat and pvalue
+        stat, pvalue, _ = stats.multiscale_graphcorr(x, y, workers=2)
+        assert_approx_equal(stat, 0.97, significant=1)
+        assert_approx_equal(pvalue, 0.001, significant=1)
+
+    @pytest.mark.xslow
+    def test_random_state(self):
+        # generate x and y
+        x, y = self._simulations(samps=100, dims=1, sim_type="linear")
+
+        # test stat and pvalue
+        stat, pvalue, _ = stats.multiscale_graphcorr(x, y, random_state=1)
+        assert_approx_equal(stat, 0.97, significant=1)
+        assert_approx_equal(pvalue, 0.001, significant=1)
+
+    @pytest.mark.xslow
+    def test_dist_perm(self):
+        np.random.seed(12345678)
+        # generate x and y
+        x, y = self._simulations(samps=100, dims=1, sim_type="nonlinear")
+        distx = cdist(x, x, metric="euclidean")
+        disty = cdist(y, y, metric="euclidean")
+
+        stat_dist, pvalue_dist, _ = stats.multiscale_graphcorr(distx, disty,
+                                                               compute_distance=None,
+                                                               random_state=1)
+        assert_approx_equal(stat_dist, 0.163, significant=1)
+        assert_approx_equal(pvalue_dist, 0.001, significant=1)
+
+    @pytest.mark.fail_slow(10)  # all other tests are XSLOW; we need at least one to run
+    @pytest.mark.slow
+    def test_pvalue_literature(self):
+        np.random.seed(12345678)
+
+        # generate x and y
+        x, y = self._simulations(samps=100, dims=1, sim_type="linear")
+
+        # test stat and pvalue
+        _, pvalue, _ = stats.multiscale_graphcorr(x, y, random_state=1)
+        assert_allclose(pvalue, 1/1001)
+
+    @pytest.mark.xslow
+    def test_alias(self):
+        np.random.seed(12345678)
+
+        # generate x and y
+        x, y = self._simulations(samps=100, dims=1, sim_type="linear")
+
+        res = stats.multiscale_graphcorr(x, y, random_state=1)
+        assert_equal(res.stat, res.statistic)

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_mstats_basic.py

@@ -0,0 +1,2066 @@
+"""
+Tests for the stats.mstats module (support for masked arrays)
+"""
+import warnings
+import platform
+
+import numpy as np
+from numpy import nan
+import numpy.ma as ma
+from numpy.ma import masked, nomask
+
+import scipy.stats.mstats as mstats
+from scipy import stats
+from .common_tests import check_named_results
+import pytest
+from pytest import raises as assert_raises
+from numpy.ma.testutils import (assert_equal, assert_almost_equal,
+                                assert_array_almost_equal,
+                                assert_array_almost_equal_nulp, assert_,
+                                assert_allclose, assert_array_equal)
+from numpy.testing import suppress_warnings
+from scipy.stats import _mstats_basic, _stats_py
+from scipy.conftest import skip_xp_invalid_arg
+from scipy.stats._axis_nan_policy import SmallSampleWarning, too_small_1d_not_omit
+
+class TestMquantiles:
+    def test_mquantiles_limit_keyword(self):
+        # Regression test for Trac ticket #867
+        data = np.array([[6., 7., 1.],
+                         [47., 15., 2.],
+                         [49., 36., 3.],
+                         [15., 39., 4.],
+                         [42., 40., -999.],
+                         [41., 41., -999.],
+                         [7., -999., -999.],
+                         [39., -999., -999.],
+                         [43., -999., -999.],
+                         [40., -999., -999.],
+                         [36., -999., -999.]])
+        desired = [[19.2, 14.6, 1.45],
+                   [40.0, 37.5, 2.5],
+                   [42.8, 40.05, 3.55]]
+        quants = mstats.mquantiles(data, axis=0, limit=(0, 50))
+        assert_almost_equal(quants, desired)
+
+
+def check_equal_gmean(array_like, desired, axis=None, dtype=None, rtol=1e-7):
+    # Note this doesn't test when axis is not specified
+    x = mstats.gmean(array_like, axis=axis, dtype=dtype)
+    assert_allclose(x, desired, rtol=rtol)
+    assert_equal(x.dtype, dtype)
+
+
+def check_equal_hmean(array_like, desired, axis=None, dtype=None, rtol=1e-7):
+    x = stats.hmean(array_like, axis=axis, dtype=dtype)
+    assert_allclose(x, desired, rtol=rtol)
+    assert_equal(x.dtype, dtype)
+
+
+@skip_xp_invalid_arg
+class TestGeoMean:
+    def test_1d(self):
+        a = [1, 2, 3, 4]
+        desired = np.power(1*2*3*4, 1./4.)
+        check_equal_gmean(a, desired, rtol=1e-14)
+
+    def test_1d_ma(self):
+        #  Test a 1d masked array
+        a = ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 100])
+        desired = 45.2872868812
+        check_equal_gmean(a, desired)
+
+        a = ma.array([1, 2, 3, 4], mask=[0, 0, 0, 1])
+        desired = np.power(1*2*3, 1./3.)
+        check_equal_gmean(a, desired, rtol=1e-14)
+
+    def test_1d_ma_value(self):
+        #  Test a 1d masked array with a masked value
+        a = np.ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 100],
+                        mask=[0, 0, 0, 0, 0, 0, 0, 0, 0, 1])
+        desired = 41.4716627439
+        check_equal_gmean(a, desired)
+
+    def test_1d_ma0(self):
+        #  Test a 1d masked array with zero element
+        a = np.ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 0])
+        desired = 0
+        check_equal_gmean(a, desired)
+
+    def test_1d_ma_inf(self):
+        #  Test a 1d masked array with negative element
+        a = np.ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, -1])
+        desired = np.nan
+        with np.errstate(invalid='ignore'):
+            check_equal_gmean(a, desired)
+
+    @pytest.mark.skipif(not hasattr(np, 'float96'),
+                        reason='cannot find float96 so skipping')
+    def test_1d_float96(self):
+        a = ma.array([1, 2, 3, 4], mask=[0, 0, 0, 1])
+        desired_dt = np.power(1*2*3, 1./3.).astype(np.float96)
+        check_equal_gmean(a, desired_dt, dtype=np.float96, rtol=1e-14)
+
+    def test_2d_ma(self):
+        a = ma.array([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]],
+                     mask=[[0, 0, 0, 0], [1, 0, 0, 1], [0, 1, 1, 0]])
+        desired = np.array([1, 2, 3, 4])
+        check_equal_gmean(a, desired, axis=0, rtol=1e-14)
+
+        desired = ma.array([np.power(1*2*3*4, 1./4.),
+                            np.power(2*3, 1./2.),
+                            np.power(1*4, 1./2.)])
+        check_equal_gmean(a, desired, axis=-1, rtol=1e-14)
+
+        #  Test a 2d masked array
+        a = [[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = 52.8885199
+        check_equal_gmean(np.ma.array(a), desired)
+
+
+@skip_xp_invalid_arg
+class TestHarMean:
+    def test_1d(self):
+        a = ma.array([1, 2, 3, 4], mask=[0, 0, 0, 1])
+        desired = 3. / (1./1 + 1./2 + 1./3)
+        check_equal_hmean(a, desired, rtol=1e-14)
+
+        a = np.ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 100])
+        desired = 34.1417152147
+        check_equal_hmean(a, desired)
+
+        a = np.ma.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 100],
+                        mask=[0, 0, 0, 0, 0, 0, 0, 0, 0, 1])
+        desired = 31.8137186141
+        check_equal_hmean(a, desired)
+
+    @pytest.mark.skipif(not hasattr(np, 'float96'),
+                        reason='cannot find float96 so skipping')
+    def test_1d_float96(self):
+        a = ma.array([1, 2, 3, 4], mask=[0, 0, 0, 1])
+        desired_dt = np.asarray(3. / (1./1 + 1./2 + 1./3), dtype=np.float96)
+        check_equal_hmean(a, desired_dt, dtype=np.float96)
+
+    def test_2d(self):
+        a = ma.array([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]],
+                     mask=[[0, 0, 0, 0], [1, 0, 0, 1], [0, 1, 1, 0]])
+        desired = ma.array([1, 2, 3, 4])
+        check_equal_hmean(a, desired, axis=0, rtol=1e-14)
+
+        desired = [4./(1/1.+1/2.+1/3.+1/4.), 2./(1/2.+1/3.), 2./(1/1.+1/4.)]
+        check_equal_hmean(a, desired, axis=-1, rtol=1e-14)
+
+        a = [[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]
+        desired = 38.6696271841
+        check_equal_hmean(np.ma.array(a), desired)
+
+
+class TestRanking:
+    def test_ranking(self):
+        x = ma.array([0,1,1,1,2,3,4,5,5,6,])
+        assert_almost_equal(mstats.rankdata(x),
+                            [1,3,3,3,5,6,7,8.5,8.5,10])
+        x[[3,4]] = masked
+        assert_almost_equal(mstats.rankdata(x),
+                            [1,2.5,2.5,0,0,4,5,6.5,6.5,8])
+        assert_almost_equal(mstats.rankdata(x, use_missing=True),
+                            [1,2.5,2.5,4.5,4.5,4,5,6.5,6.5,8])
+        x = ma.array([0,1,5,1,2,4,3,5,1,6,])
+        assert_almost_equal(mstats.rankdata(x),
+                            [1,3,8.5,3,5,7,6,8.5,3,10])
+        x = ma.array([[0,1,1,1,2], [3,4,5,5,6,]])
+        assert_almost_equal(mstats.rankdata(x),
+                            [[1,3,3,3,5], [6,7,8.5,8.5,10]])
+        assert_almost_equal(mstats.rankdata(x, axis=1),
+                            [[1,3,3,3,5], [1,2,3.5,3.5,5]])
+        assert_almost_equal(mstats.rankdata(x,axis=0),
+                            [[1,1,1,1,1], [2,2,2,2,2,]])
+
+
+class TestCorr:
+    def test_pearsonr(self):
+        # Tests some computations of Pearson's r
+        x = ma.arange(10)
+        with warnings.catch_warnings():
+            # The tests in this context are edge cases, with perfect
+            # correlation or anticorrelation, or totally masked data.
+            # None of these should trigger a RuntimeWarning.
+            warnings.simplefilter("error", RuntimeWarning)
+
+            assert_almost_equal(mstats.pearsonr(x, x)[0], 1.0)
+            assert_almost_equal(mstats.pearsonr(x, x[::-1])[0], -1.0)
+
+            x = ma.array(x, mask=True)
+            pr = mstats.pearsonr(x, x)
+            assert_(pr[0] is masked)
+            assert_(pr[1] is masked)
+
+        x1 = ma.array([-1.0, 0.0, 1.0])
+        y1 = ma.array([0, 0, 3])
+        r, p = mstats.pearsonr(x1, y1)
+        assert_almost_equal(r, np.sqrt(3)/2)
+        assert_almost_equal(p, 1.0/3)
+
+        # (x2, y2) have the same unmasked data as (x1, y1).
+        mask = [False, False, False, True]
+        x2 = ma.array([-1.0, 0.0, 1.0, 99.0], mask=mask)
+        y2 = ma.array([0, 0, 3, -1], mask=mask)
+        r, p = mstats.pearsonr(x2, y2)
+        assert_almost_equal(r, np.sqrt(3)/2)
+        assert_almost_equal(p, 1.0/3)
+
+    def test_pearsonr_misaligned_mask(self):
+        mx = np.ma.masked_array([1, 2, 3, 4, 5, 6], mask=[0, 1, 0, 0, 0, 0])
+        my = np.ma.masked_array([9, 8, 7, 6, 5, 9], mask=[0, 0, 1, 0, 0, 0])
+        x = np.array([1, 4, 5, 6])
+        y = np.array([9, 6, 5, 9])
+        mr, mp = mstats.pearsonr(mx, my)
+        r, p = stats.pearsonr(x, y)
+        assert_equal(mr, r)
+        assert_equal(mp, p)
+
+    def test_spearmanr(self):
+        # Tests some computations of Spearman's rho
+        (x, y) = ([5.05,6.75,3.21,2.66], [1.65,2.64,2.64,6.95])
+        assert_almost_equal(mstats.spearmanr(x,y)[0], -0.6324555)
+        (x, y) = ([5.05,6.75,3.21,2.66,np.nan],[1.65,2.64,2.64,6.95,np.nan])
+        (x, y) = (ma.fix_invalid(x), ma.fix_invalid(y))
+        assert_almost_equal(mstats.spearmanr(x,y)[0], -0.6324555)
+
+        x = [2.0, 47.4, 42.0, 10.8, 60.1, 1.7, 64.0, 63.1,
+             1.0, 1.4, 7.9, 0.3, 3.9, 0.3, 6.7]
+        y = [22.6, 8.3, 44.4, 11.9, 24.6, 0.6, 5.7, 41.6,
+             0.0, 0.6, 6.7, 3.8, 1.0, 1.2, 1.4]
+        assert_almost_equal(mstats.spearmanr(x,y)[0], 0.6887299)
+        x = [2.0, 47.4, 42.0, 10.8, 60.1, 1.7, 64.0, 63.1,
+             1.0, 1.4, 7.9, 0.3, 3.9, 0.3, 6.7, np.nan]
+        y = [22.6, 8.3, 44.4, 11.9, 24.6, 0.6, 5.7, 41.6,
+             0.0, 0.6, 6.7, 3.8, 1.0, 1.2, 1.4, np.nan]
+        (x, y) = (ma.fix_invalid(x), ma.fix_invalid(y))
+        assert_almost_equal(mstats.spearmanr(x,y)[0], 0.6887299)
+        # Next test is to make sure calculation uses sufficient precision.
+        # The denominator's value is ~n^3 and used to be represented as an
+        # int. 2000**3 > 2**32 so these arrays would cause overflow on
+        # some machines.
+        x = list(range(2000))
+        y = list(range(2000))
+        y[0], y[9] = y[9], y[0]
+        y[10], y[434] = y[434], y[10]
+        y[435], y[1509] = y[1509], y[435]
+        # rho = 1 - 6 * (2 * (9^2 + 424^2 + 1074^2))/(2000 * (2000^2 - 1))
+        #     = 1 - (1 / 500)
+        #     = 0.998
+        assert_almost_equal(mstats.spearmanr(x,y)[0], 0.998)
+
+        # test for namedtuple attributes
+        res = mstats.spearmanr(x, y)
+        attributes = ('correlation', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_spearmanr_alternative(self):
+        # check against R
+        # options(digits=16)
+        # cor.test(c(2.0, 47.4, 42.0, 10.8, 60.1, 1.7, 64.0, 63.1,
+        #            1.0, 1.4, 7.9, 0.3, 3.9, 0.3, 6.7),
+        #          c(22.6, 8.3, 44.4, 11.9, 24.6, 0.6, 5.7, 41.6,
+        #            0.0, 0.6, 6.7, 3.8, 1.0, 1.2, 1.4),
+        #          alternative='two.sided', method='spearman')
+        x = [2.0, 47.4, 42.0, 10.8, 60.1, 1.7, 64.0, 63.1,
+             1.0, 1.4, 7.9, 0.3, 3.9, 0.3, 6.7]
+        y = [22.6, 8.3, 44.4, 11.9, 24.6, 0.6, 5.7, 41.6,
+             0.0, 0.6, 6.7, 3.8, 1.0, 1.2, 1.4]
+
+        r_exp = 0.6887298747763864  # from cor.test
+
+        r, p = mstats.spearmanr(x, y)
+        assert_allclose(r, r_exp)
+        assert_allclose(p, 0.004519192910756)
+
+        r, p = mstats.spearmanr(x, y, alternative='greater')
+        assert_allclose(r, r_exp)
+        assert_allclose(p, 0.002259596455378)
+
+        r, p = mstats.spearmanr(x, y, alternative='less')
+        assert_allclose(r, r_exp)
+        assert_allclose(p, 0.9977404035446)
+
+        # intuitive test (with obvious positive correlation)
+        n = 100
+        x = np.linspace(0, 5, n)
+        y = 0.1*x + np.random.rand(n)  # y is positively correlated w/ x
+
+        stat1, p1 = mstats.spearmanr(x, y)
+
+        stat2, p2 = mstats.spearmanr(x, y, alternative="greater")
+        assert_allclose(p2, p1 / 2)  # positive correlation -> small p
+
+        stat3, p3 = mstats.spearmanr(x, y, alternative="less")
+        assert_allclose(p3, 1 - p1 / 2)  # positive correlation -> large p
+
+        assert stat1 == stat2 == stat3
+
+        with pytest.raises(ValueError, match="alternative must be 'less'..."):
+            mstats.spearmanr(x, y, alternative="ekki-ekki")
+
+    @pytest.mark.skipif(platform.machine() == 'ppc64le',
+                        reason="fails/crashes on ppc64le")
+    def test_kendalltau(self):
+        # check case with maximum disorder and p=1
+        x = ma.array(np.array([9, 2, 5, 6]))
+        y = ma.array(np.array([4, 7, 9, 11]))
+        # Cross-check with exact result from R:
+        # cor.test(x,y,method="kendall",exact=1)
+        expected = [0.0, 1.0]
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
+
+        # simple case without ties
+        x = ma.array(np.arange(10))
+        y = ma.array(np.arange(10))
+        # Cross-check with exact result from R:
+        # cor.test(x,y,method="kendall",exact=1)
+        expected = [1.0, 5.511463844797e-07]
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
+
+        # check exception in case of invalid method keyword
+        assert_raises(ValueError, mstats.kendalltau, x, y, method='banana')
+
+        # swap a couple of values
+        b = y[1]
+        y[1] = y[2]
+        y[2] = b
+        # Cross-check with exact result from R:
+        # cor.test(x,y,method="kendall",exact=1)
+        expected = [0.9555555555555556, 5.511463844797e-06]
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
+
+        # swap a couple more
+        b = y[5]
+        y[5] = y[6]
+        y[6] = b
+        # Cross-check with exact result from R:
+        # cor.test(x,y,method="kendall",exact=1)
+        expected = [0.9111111111111111, 2.976190476190e-05]
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
+
+        # same in opposite direction
+        x = ma.array(np.arange(10))
+        y = ma.array(np.arange(10)[::-1])
+        # Cross-check with exact result from R:
+        # cor.test(x,y,method="kendall",exact=1)
+        expected = [-1.0, 5.511463844797e-07]
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
+
+        # swap a couple of values
+        b = y[1]
+        y[1] = y[2]
+        y[2] = b
+        # Cross-check with exact result from R:
+        # cor.test(x,y,method="kendall",exact=1)
+        expected = [-0.9555555555555556, 5.511463844797e-06]
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
+
+        # swap a couple more
+        b = y[5]
+        y[5] = y[6]
+        y[6] = b
+        # Cross-check with exact result from R:
+        # cor.test(x,y,method="kendall",exact=1)
+        expected = [-0.9111111111111111, 2.976190476190e-05]
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)), expected)
+
+        # Tests some computations of Kendall's tau
+        x = ma.fix_invalid([5.05, 6.75, 3.21, 2.66, np.nan])
+        y = ma.fix_invalid([1.65, 26.5, -5.93, 7.96, np.nan])
+        z = ma.fix_invalid([1.65, 2.64, 2.64, 6.95, np.nan])
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y)),
+                            [+0.3333333, 0.75])
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, y, method='asymptotic')),
+                            [+0.3333333, 0.4969059])
+        assert_almost_equal(np.asarray(mstats.kendalltau(x, z)),
+                            [-0.5477226, 0.2785987])
+        #
+        x = ma.fix_invalid([0, 0, 0, 0, 20, 20, 0, 60, 0, 20,
+                            10, 10, 0, 40, 0, 20, 0, 0, 0, 0, 0, np.nan])
+        y = ma.fix_invalid([0, 80, 80, 80, 10, 33, 60, 0, 67, 27,
+                            25, 80, 80, 80, 80, 80, 80, 0, 10, 45, np.nan, 0])
+        result = mstats.kendalltau(x, y)
+        assert_almost_equal(np.asarray(result), [-0.1585188, 0.4128009])
+
+        # test for namedtuple attributes
+        attributes = ('correlation', 'pvalue')
+        check_named_results(result, attributes, ma=True)
+
+    @pytest.mark.skipif(platform.machine() == 'ppc64le',
+                        reason="fails/crashes on ppc64le")
+    @pytest.mark.slow
+    def test_kendalltau_large(self):
+        # make sure internal variable use correct precision with
+        # larger arrays
+        x = np.arange(2000, dtype=float)
+        x = ma.masked_greater(x, 1995)
+        y = np.arange(2000, dtype=float)
+        y = np.concatenate((y[1000:], y[:1000]))
+        assert_(np.isfinite(mstats.kendalltau(x, y)[1]))
+
+    def test_kendalltau_seasonal(self):
+        # Tests the seasonal Kendall tau.
+        x = [[nan, nan, 4, 2, 16, 26, 5, 1, 5, 1, 2, 3, 1],
+             [4, 3, 5, 3, 2, 7, 3, 1, 1, 2, 3, 5, 3],
+             [3, 2, 5, 6, 18, 4, 9, 1, 1, nan, 1, 1, nan],
+             [nan, 6, 11, 4, 17, nan, 6, 1, 1, 2, 5, 1, 1]]
+        x = ma.fix_invalid(x).T
+        output = mstats.kendalltau_seasonal(x)
+        assert_almost_equal(output['global p-value (indep)'], 0.008, 3)
+        assert_almost_equal(output['seasonal p-value'].round(2),
+                            [0.18,0.53,0.20,0.04])
+
+    @pytest.mark.parametrize("method", ("exact", "asymptotic"))
+    @pytest.mark.parametrize("alternative", ("two-sided", "greater", "less"))
+    def test_kendalltau_mstats_vs_stats(self, method, alternative):
+        # Test that mstats.kendalltau and stats.kendalltau with
+        # nan_policy='omit' matches behavior of stats.kendalltau
+        # Accuracy of the alternatives is tested in stats/tests/test_stats.py
+
+        np.random.seed(0)
+        n = 50
+        x = np.random.rand(n)
+        y = np.random.rand(n)
+        mask = np.random.rand(n) > 0.5
+
+        x_masked = ma.array(x, mask=mask)
+        y_masked = ma.array(y, mask=mask)
+        res_masked = mstats.kendalltau(
+            x_masked, y_masked, method=method, alternative=alternative)
+
+        x_compressed = x_masked.compressed()
+        y_compressed = y_masked.compressed()
+        res_compressed = stats.kendalltau(
+            x_compressed, y_compressed, method=method, alternative=alternative)
+
+        x[mask] = np.nan
+        y[mask] = np.nan
+        res_nan = stats.kendalltau(
+            x, y, method=method, nan_policy='omit', alternative=alternative)
+
+        assert_allclose(res_masked, res_compressed)
+        assert_allclose(res_nan, res_compressed)
+
+    def test_kendall_p_exact_medium(self):
+        # Test for the exact method with medium samples (some n >= 171)
+        # expected values generated using SymPy
+        expectations = {(100, 2393): 0.62822615287956040664,
+                        (101, 2436): 0.60439525773513602669,
+                        (170, 0): 2.755801935583541e-307,
+                        (171, 0): 0.0,
+                        (171, 1): 2.755801935583541e-307,
+                        (172, 1): 0.0,
+                        (200, 9797): 0.74753983745929675209,
+                        (201, 9656): 0.40959218958120363618}
+        for nc, expected in expectations.items():
+            res = _mstats_basic._kendall_p_exact(nc[0], nc[1])
+            assert_almost_equal(res, expected)
+
+    @pytest.mark.xslow
+    def test_kendall_p_exact_large(self):
+        # Test for the exact method with large samples (n >= 171)
+        # expected values generated using SymPy
+        expectations = {(400, 38965): 0.48444283672113314099,
+                        (401, 39516): 0.66363159823474837662,
+                        (800, 156772): 0.42265448483120932055,
+                        (801, 157849): 0.53437553412194416236,
+                        (1600, 637472): 0.84200727400323538419,
+                        (1601, 630304): 0.34465255088058593946}
+
+        for nc, expected in expectations.items():
+            res = _mstats_basic._kendall_p_exact(nc[0], nc[1])
+            assert_almost_equal(res, expected)
+
+    def test_pointbiserial(self):
+        x = [1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0,
+             0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, -1]
+        y = [14.8, 13.8, 12.4, 10.1, 7.1, 6.1, 5.8, 4.6, 4.3, 3.5, 3.3, 3.2,
+             3.0, 2.8, 2.8, 2.5, 2.4, 2.3, 2.1, 1.7, 1.7, 1.5, 1.3, 1.3, 1.2,
+             1.2, 1.1, 0.8, 0.7, 0.6, 0.5, 0.2, 0.2, 0.1, np.nan]
+        assert_almost_equal(mstats.pointbiserialr(x, y)[0], 0.36149, 5)
+
+        # test for namedtuple attributes
+        res = mstats.pointbiserialr(x, y)
+        attributes = ('correlation', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+
+@skip_xp_invalid_arg
+class TestTrimming:
+
+    def test_trim(self):
+        a = ma.arange(10)
+        assert_equal(mstats.trim(a), [0,1,2,3,4,5,6,7,8,9])
+        a = ma.arange(10)
+        assert_equal(mstats.trim(a,(2,8)), [None,None,2,3,4,5,6,7,8,None])
+        a = ma.arange(10)
+        assert_equal(mstats.trim(a,limits=(2,8),inclusive=(False,False)),
+                     [None,None,None,3,4,5,6,7,None,None])
+        a = ma.arange(10)
+        assert_equal(mstats.trim(a,limits=(0.1,0.2),relative=True),
+                     [None,1,2,3,4,5,6,7,None,None])
+
+        a = ma.arange(12)
+        a[[0,-1]] = a[5] = masked
+        assert_equal(mstats.trim(a, (2,8)),
+                     [None, None, 2, 3, 4, None, 6, 7, 8, None, None, None])
+
+        x = ma.arange(100).reshape(10, 10)
+        expected = [1]*10 + [0]*70 + [1]*20
+        trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=None)
+        assert_equal(trimx._mask.ravel(), expected)
+        trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=0)
+        assert_equal(trimx._mask.ravel(), expected)
+        trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=-1)
+        assert_equal(trimx._mask.T.ravel(), expected)
+
+        # same as above, but with an extra masked row inserted
+        x = ma.arange(110).reshape(11, 10)
+        x[1] = masked
+        expected = [1]*20 + [0]*70 + [1]*20
+        trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=None)
+        assert_equal(trimx._mask.ravel(), expected)
+        trimx = mstats.trim(x, (0.1,0.2), relative=True, axis=0)
+        assert_equal(trimx._mask.ravel(), expected)
+        trimx = mstats.trim(x.T, (0.1,0.2), relative=True, axis=-1)
+        assert_equal(trimx.T._mask.ravel(), expected)
+
+    def test_trim_old(self):
+        x = ma.arange(100)
+        assert_equal(mstats.trimboth(x).count(), 60)
+        assert_equal(mstats.trimtail(x,tail='r').count(), 80)
+        x[50:70] = masked
+        trimx = mstats.trimboth(x)
+        assert_equal(trimx.count(), 48)
+        assert_equal(trimx._mask, [1]*16 + [0]*34 + [1]*20 + [0]*14 + [1]*16)
+        x._mask = nomask
+        x.shape = (10,10)
+        assert_equal(mstats.trimboth(x).count(), 60)
+        assert_equal(mstats.trimtail(x).count(), 80)
+
+    def test_trimr(self):
+        x = ma.arange(10)
+        result = mstats.trimr(x, limits=(0.15, 0.14), inclusive=(False, False))
+        expected = ma.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
+                            mask=[1, 1, 0, 0, 0, 0, 0, 0, 0, 1])
+        assert_equal(result, expected)
+        assert_equal(result.mask, expected.mask)
+
+    def test_trimmedmean(self):
+        data = ma.array([77, 87, 88,114,151,210,219,246,253,262,
+                         296,299,306,376,428,515,666,1310,2611])
+        assert_almost_equal(mstats.trimmed_mean(data,0.1), 343, 0)
+        assert_almost_equal(mstats.trimmed_mean(data,(0.1,0.1)), 343, 0)
+        assert_almost_equal(mstats.trimmed_mean(data,(0.2,0.2)), 283, 0)
+
+    def test_trimmedvar(self):
+        # Basic test. Additional tests of all arguments, edge cases,
+        # input validation, and proper treatment of masked arrays are needed.
+        rng = np.random.default_rng(3262323289434724460)
+        data_orig = rng.random(size=20)
+        data = np.sort(data_orig)
+        data = ma.array(data, mask=[1, 1, 0, 0, 0, 0, 0, 0, 0, 0,
+                                    0, 0, 0, 0, 0, 0, 0, 0, 1, 1])
+        assert_allclose(mstats.trimmed_var(data_orig, 0.1), data.var())
+
+    def test_trimmedstd(self):
+        # Basic test. Additional tests of all arguments, edge cases,
+        # input validation, and proper treatment of masked arrays are needed.
+        rng = np.random.default_rng(7121029245207162780)
+        data_orig = rng.random(size=20)
+        data = np.sort(data_orig)
+        data = ma.array(data, mask=[1, 1, 0, 0, 0, 0, 0, 0, 0, 0,
+                                    0, 0, 0, 0, 0, 0, 0, 0, 1, 1])
+        assert_allclose(mstats.trimmed_std(data_orig, 0.1), data.std())
+
+    def test_trimmed_stde(self):
+        data = ma.array([77, 87, 88,114,151,210,219,246,253,262,
+                         296,299,306,376,428,515,666,1310,2611])
+        assert_almost_equal(mstats.trimmed_stde(data,(0.2,0.2)), 56.13193, 5)
+        assert_almost_equal(mstats.trimmed_stde(data,0.2), 56.13193, 5)
+
+    def test_winsorization(self):
+        data = ma.array([77, 87, 88,114,151,210,219,246,253,262,
+                         296,299,306,376,428,515,666,1310,2611])
+        assert_almost_equal(mstats.winsorize(data,(0.2,0.2)).var(ddof=1),
+                            21551.4, 1)
+        assert_almost_equal(
+            mstats.winsorize(data, (0.2,0.2),(False,False)).var(ddof=1),
+            11887.3, 1)
+        data[5] = masked
+        winsorized = mstats.winsorize(data)
+        assert_equal(winsorized.mask, data.mask)
+
+    def test_winsorization_nan(self):
+        data = ma.array([np.nan, np.nan, 0, 1, 2])
+        assert_raises(ValueError, mstats.winsorize, data, (0.05, 0.05),
+                      nan_policy='raise')
+        # Testing propagate (default behavior)
+        assert_equal(mstats.winsorize(data, (0.4, 0.4)),
+                     ma.array([2, 2, 2, 2, 2]))
+        assert_equal(mstats.winsorize(data, (0.8, 0.8)),
+                     ma.array([np.nan, np.nan, np.nan, np.nan, np.nan]))
+        assert_equal(mstats.winsorize(data, (0.4, 0.4), nan_policy='omit'),
+                     ma.array([np.nan, np.nan, 2, 2, 2]))
+        assert_equal(mstats.winsorize(data, (0.8, 0.8), nan_policy='omit'),
+                     ma.array([np.nan, np.nan, 2, 2, 2]))
+
+
+@skip_xp_invalid_arg
+class TestMoments:
+    # Comparison numbers are found using R v.1.5.1
+    # note that length(testcase) = 4
+    # testmathworks comes from documentation for the
+    # Statistics Toolbox for Matlab and can be found at both
+    # https://www.mathworks.com/help/stats/kurtosis.html
+    # https://www.mathworks.com/help/stats/skewness.html
+    # Note that both test cases came from here.
+    testcase = [1,2,3,4]
+    testmathworks = ma.fix_invalid([1.165, 0.6268, 0.0751, 0.3516, -0.6965,
+                                    np.nan])
+    testcase_2d = ma.array(
+        np.array([[0.05245846, 0.50344235, 0.86589117, 0.36936353, 0.46961149],
+                  [0.11574073, 0.31299969, 0.45925772, 0.72618805, 0.75194407],
+                  [0.67696689, 0.91878127, 0.09769044, 0.04645137, 0.37615733],
+                  [0.05903624, 0.29908861, 0.34088298, 0.66216337, 0.83160998],
+                  [0.64619526, 0.94894632, 0.27855892, 0.0706151, 0.39962917]]),
+        mask=np.array([[True, False, False, True, False],
+                       [True, True, True, False, True],
+                       [False, False, False, False, False],
+                       [True, True, True, True, True],
+                       [False, False, True, False, False]], dtype=bool))
+
+    def _assert_equal(self, actual, expect, *, shape=None, dtype=None):
+        expect = np.asarray(expect)
+        if shape is not None:
+            expect = np.broadcast_to(expect, shape)
+        assert_array_equal(actual, expect)
+        if dtype is None:
+            dtype = expect.dtype
+        assert actual.dtype == dtype
+
+    def test_moment(self):
+        y = mstats.moment(self.testcase,1)
+        assert_almost_equal(y,0.0,10)
+        y = mstats.moment(self.testcase,2)
+        assert_almost_equal(y,1.25)
+        y = mstats.moment(self.testcase,3)
+        assert_almost_equal(y,0.0)
+        y = mstats.moment(self.testcase,4)
+        assert_almost_equal(y,2.5625)
+
+        # check array_like input for moment
+        y = mstats.moment(self.testcase, [1, 2, 3, 4])
+        assert_allclose(y, [0, 1.25, 0, 2.5625])
+
+        # check moment input consists only of integers
+        y = mstats.moment(self.testcase, 0.0)
+        assert_allclose(y, 1.0)
+        assert_raises(ValueError, mstats.moment, self.testcase, 1.2)
+        y = mstats.moment(self.testcase, [1.0, 2, 3, 4.0])
+        assert_allclose(y, [0, 1.25, 0, 2.5625])
+
+        # test empty input
+        y = mstats.moment([])
+        self._assert_equal(y, np.nan, dtype=np.float64)
+        y = mstats.moment(np.array([], dtype=np.float32))
+        self._assert_equal(y, np.nan, dtype=np.float32)
+        y = mstats.moment(np.zeros((1, 0)), axis=0)
+        self._assert_equal(y, [], shape=(0,), dtype=np.float64)
+        y = mstats.moment([[]], axis=1)
+        self._assert_equal(y, np.nan, shape=(1,), dtype=np.float64)
+        y = mstats.moment([[]], moment=[0, 1], axis=0)
+        self._assert_equal(y, [], shape=(2, 0))
+
+        x = np.arange(10.)
+        x[9] = np.nan
+        assert_equal(mstats.moment(x, 2), ma.masked)  # NaN value is ignored
+
+    def test_variation(self):
+        y = mstats.variation(self.testcase)
+        assert_almost_equal(y,0.44721359549996, 10)
+
+    def test_variation_ddof(self):
+        # test variation with delta degrees of freedom
+        # regression test for gh-13341
+        a = np.array([1, 2, 3, 4, 5])
+        y = mstats.variation(a, ddof=1)
+        assert_almost_equal(y, 0.5270462766947299)
+
+    def test_skewness(self):
+        y = mstats.skew(self.testmathworks)
+        assert_almost_equal(y,-0.29322304336607,10)
+        y = mstats.skew(self.testmathworks,bias=0)
+        assert_almost_equal(y,-0.437111105023940,10)
+        y = mstats.skew(self.testcase)
+        assert_almost_equal(y,0.0,10)
+
+        # test that skew works on multidimensional masked arrays
+        correct_2d = ma.array(
+            np.array([0.6882870394455785, 0, 0.2665647526856708,
+                      0, -0.05211472114254485]),
+            mask=np.array([False, False, False, True, False], dtype=bool)
+        )
+        assert_allclose(mstats.skew(self.testcase_2d, 1), correct_2d)
+        for i, row in enumerate(self.testcase_2d):
+            assert_almost_equal(mstats.skew(row), correct_2d[i])
+
+        correct_2d_bias_corrected = ma.array(
+            np.array([1.685952043212545, 0.0, 0.3973712716070531, 0,
+                      -0.09026534484117164]),
+            mask=np.array([False, False, False, True, False], dtype=bool)
+        )
+        assert_allclose(mstats.skew(self.testcase_2d, 1, bias=False),
+                        correct_2d_bias_corrected)
+        for i, row in enumerate(self.testcase_2d):
+            assert_almost_equal(mstats.skew(row, bias=False),
+                                correct_2d_bias_corrected[i])
+
+        # Check consistency between stats and mstats implementations
+        assert_allclose(mstats.skew(self.testcase_2d[2, :]),
+                        stats.skew(self.testcase_2d[2, :]))
+
+    def test_kurtosis(self):
+        # Set flags for axis = 0 and fisher=0 (Pearson's definition of kurtosis
+        # for compatibility with Matlab)
+        y = mstats.kurtosis(self.testmathworks, 0, fisher=0, bias=1)
+        assert_almost_equal(y, 2.1658856802973, 10)
+        # Note that MATLAB has confusing docs for the following case
+        #  kurtosis(x,0) gives an unbiased estimate of Pearson's skewness
+        #  kurtosis(x) gives a biased estimate of Fisher's skewness (Pearson-3)
+        #  The MATLAB docs imply that both should give Fisher's
+        y = mstats.kurtosis(self.testmathworks, fisher=0, bias=0)
+        assert_almost_equal(y, 3.663542721189047, 10)
+        y = mstats.kurtosis(self.testcase, 0, 0)
+        assert_almost_equal(y, 1.64)
+
+        # test that kurtosis works on multidimensional masked arrays
+        correct_2d = ma.array(np.array([-1.5, -3., -1.47247052385, 0.,
+                                        -1.26979517952]),
+                              mask=np.array([False, False, False, True,
+                                             False], dtype=bool))
+        assert_array_almost_equal(mstats.kurtosis(self.testcase_2d, 1),
+                                  correct_2d)
+        for i, row in enumerate(self.testcase_2d):
+            assert_almost_equal(mstats.kurtosis(row), correct_2d[i])
+
+        correct_2d_bias_corrected = ma.array(
+            np.array([-1.5, -3., -1.88988209538, 0., -0.5234638463918877]),
+            mask=np.array([False, False, False, True, False], dtype=bool))
+        assert_array_almost_equal(mstats.kurtosis(self.testcase_2d, 1,
+                                                  bias=False),
+                                  correct_2d_bias_corrected)
+        for i, row in enumerate(self.testcase_2d):
+            assert_almost_equal(mstats.kurtosis(row, bias=False),
+                                correct_2d_bias_corrected[i])
+
+        # Check consistency between stats and mstats implementations
+        assert_array_almost_equal_nulp(mstats.kurtosis(self.testcase_2d[2, :]),
+                                       stats.kurtosis(self.testcase_2d[2, :]),
+                                       nulp=4)
+
+
+class TestMode:
+    def test_mode(self):
+        a1 = [0,0,0,1,1,1,2,3,3,3,3,4,5,6,7]
+        a2 = np.reshape(a1, (3,5))
+        a3 = np.array([1,2,3,4,5,6])
+        a4 = np.reshape(a3, (3,2))
+        ma1 = ma.masked_where(ma.array(a1) > 2, a1)
+        ma2 = ma.masked_where(a2 > 2, a2)
+        ma3 = ma.masked_where(a3 < 2, a3)
+        ma4 = ma.masked_where(ma.array(a4) < 2, a4)
+        assert_equal(mstats.mode(a1, axis=None), (3,4))
+        assert_equal(mstats.mode(a1, axis=0), (3,4))
+        assert_equal(mstats.mode(ma1, axis=None), (0,3))
+        assert_equal(mstats.mode(a2, axis=None), (3,4))
+        assert_equal(mstats.mode(ma2, axis=None), (0,3))
+        assert_equal(mstats.mode(a3, axis=None), (1,1))
+        assert_equal(mstats.mode(ma3, axis=None), (2,1))
+        assert_equal(mstats.mode(a2, axis=0), ([[0,0,0,1,1]], [[1,1,1,1,1]]))
+        assert_equal(mstats.mode(ma2, axis=0), ([[0,0,0,1,1]], [[1,1,1,1,1]]))
+        assert_equal(mstats.mode(a2, axis=-1), ([[0],[3],[3]], [[3],[3],[1]]))
+        assert_equal(mstats.mode(ma2, axis=-1), ([[0],[1],[0]], [[3],[1],[0]]))
+        assert_equal(mstats.mode(ma4, axis=0), ([[3,2]], [[1,1]]))
+        assert_equal(mstats.mode(ma4, axis=-1), ([[2],[3],[5]], [[1],[1],[1]]))
+
+        a1_res = mstats.mode(a1, axis=None)
+
+        # test for namedtuple attributes
+        attributes = ('mode', 'count')
+        check_named_results(a1_res, attributes, ma=True)
+
+    def test_mode_modifies_input(self):
+        # regression test for gh-6428: mode(..., axis=None) may not modify
+        # the input array
+        im = np.zeros((100, 100))
+        im[:50, :] += 1
+        im[:, :50] += 1
+        cp = im.copy()
+        mstats.mode(im, None)
+        assert_equal(im, cp)
+
+
+class TestPercentile:
+    def setup_method(self):
+        self.a1 = [3, 4, 5, 10, -3, -5, 6]
+        self.a2 = [3, -6, -2, 8, 7, 4, 2, 1]
+        self.a3 = [3., 4, 5, 10, -3, -5, -6, 7.0]
+
+    def test_percentile(self):
+        x = np.arange(8) * 0.5
+        assert_equal(mstats.scoreatpercentile(x, 0), 0.)
+        assert_equal(mstats.scoreatpercentile(x, 100), 3.5)
+        assert_equal(mstats.scoreatpercentile(x, 50), 1.75)
+
+    def test_2D(self):
+        x = ma.array([[1, 1, 1],
+                      [1, 1, 1],
+                      [4, 4, 3],
+                      [1, 1, 1],
+                      [1, 1, 1]])
+        assert_equal(mstats.scoreatpercentile(x, 50), [1, 1, 1])
+
+
+@skip_xp_invalid_arg
+class TestVariability:
+    """  Comparison numbers are found using R v.1.5.1
+         note that length(testcase) = 4
+    """
+    testcase = ma.fix_invalid([1,2,3,4,np.nan])
+
+    def test_sem(self):
+        # This is not in R, so used: sqrt(var(testcase)*3/4) / sqrt(3)
+        y = mstats.sem(self.testcase)
+        assert_almost_equal(y, 0.6454972244)
+        n = self.testcase.count()
+        assert_allclose(mstats.sem(self.testcase, ddof=0) * np.sqrt(n/(n-2)),
+                        mstats.sem(self.testcase, ddof=2))
+
+    def test_zmap(self):
+        # This is not in R, so tested by using:
+        #    (testcase[i]-mean(testcase,axis=0)) / sqrt(var(testcase)*3/4)
+        y = mstats.zmap(self.testcase, self.testcase)
+        desired_unmaskedvals = ([-1.3416407864999, -0.44721359549996,
+                                 0.44721359549996, 1.3416407864999])
+        assert_array_almost_equal(desired_unmaskedvals,
+                                  y.data[y.mask == False], decimal=12)  # noqa: E712
+
+    def test_zscore(self):
+        # This is not in R, so tested by using:
+        #     (testcase[i]-mean(testcase,axis=0)) / sqrt(var(testcase)*3/4)
+        y = mstats.zscore(self.testcase)
+        desired = ma.fix_invalid([-1.3416407864999, -0.44721359549996,
+                                  0.44721359549996, 1.3416407864999, np.nan])
+        assert_almost_equal(desired, y, decimal=12)
+
+
+@skip_xp_invalid_arg
+class TestMisc:
+
+    def test_obrientransform(self):
+        args = [[5]*5+[6]*11+[7]*9+[8]*3+[9]*2+[10]*2,
+                [6]+[7]*2+[8]*4+[9]*9+[10]*16]
+        result = [5*[3.1828]+11*[0.5591]+9*[0.0344]+3*[1.6086]+2*[5.2817]+2*[11.0538],
+                  [10.4352]+2*[4.8599]+4*[1.3836]+9*[0.0061]+16*[0.7277]]
+        assert_almost_equal(np.round(mstats.obrientransform(*args).T, 4),
+                            result, 4)
+
+    def test_ks_2samp(self):
+        x = [[nan,nan, 4, 2, 16, 26, 5, 1, 5, 1, 2, 3, 1],
+             [4, 3, 5, 3, 2, 7, 3, 1, 1, 2, 3, 5, 3],
+             [3, 2, 5, 6, 18, 4, 9, 1, 1, nan, 1, 1, nan],
+             [nan, 6, 11, 4, 17, nan, 6, 1, 1, 2, 5, 1, 1]]
+        x = ma.fix_invalid(x).T
+        (winter, spring, summer, fall) = x.T
+
+        assert_almost_equal(np.round(mstats.ks_2samp(winter, spring), 4),
+                            (0.1818, 0.9628))
+        assert_almost_equal(np.round(mstats.ks_2samp(winter, spring, 'g'), 4),
+                            (0.1469, 0.6886))
+        assert_almost_equal(np.round(mstats.ks_2samp(winter, spring, 'l'), 4),
+                            (0.1818, 0.6011))
+
+    def test_friedmanchisq(self):
+        # No missing values
+        args = ([9.0,9.5,5.0,7.5,9.5,7.5,8.0,7.0,8.5,6.0],
+                [7.0,6.5,7.0,7.5,5.0,8.0,6.0,6.5,7.0,7.0],
+                [6.0,8.0,4.0,6.0,7.0,6.5,6.0,4.0,6.5,3.0])
+        result = mstats.friedmanchisquare(*args)
+        assert_almost_equal(result[0], 10.4737, 4)
+        assert_almost_equal(result[1], 0.005317, 6)
+        # Missing values
+        x = [[nan,nan, 4, 2, 16, 26, 5, 1, 5, 1, 2, 3, 1],
+             [4, 3, 5, 3, 2, 7, 3, 1, 1, 2, 3, 5, 3],
+             [3, 2, 5, 6, 18, 4, 9, 1, 1,nan, 1, 1,nan],
+             [nan, 6, 11, 4, 17,nan, 6, 1, 1, 2, 5, 1, 1]]
+        x = ma.fix_invalid(x)
+        result = mstats.friedmanchisquare(*x)
+        assert_almost_equal(result[0], 2.0156, 4)
+        assert_almost_equal(result[1], 0.5692, 4)
+
+        # test for namedtuple attributes
+        attributes = ('statistic', 'pvalue')
+        check_named_results(result, attributes, ma=True)
+
+
+def test_regress_simple():
+    # Regress a line with sinusoidal noise. Test for #1273.
+    x = np.linspace(0, 100, 100)
+    y = 0.2 * np.linspace(0, 100, 100) + 10
+    y += np.sin(np.linspace(0, 20, 100))
+
+    result = mstats.linregress(x, y)
+
+    # Result is of a correct class and with correct fields
+    lr = _stats_py.LinregressResult
+    assert_(isinstance(result, lr))
+    attributes = ('slope', 'intercept', 'rvalue', 'pvalue', 'stderr')
+    check_named_results(result, attributes, ma=True)
+    assert 'intercept_stderr' in dir(result)
+
+    # Slope and intercept are estimated correctly
+    assert_almost_equal(result.slope, 0.19644990055858422)
+    assert_almost_equal(result.intercept, 10.211269918932341)
+    assert_almost_equal(result.stderr, 0.002395781449783862)
+    assert_almost_equal(result.intercept_stderr, 0.13866936078570702)
+
+
+def test_linregress_identical_x():
+    x = np.zeros(10)
+    y = np.random.random(10)
+    msg = "Cannot calculate a linear regression if all x values are identical"
+    with assert_raises(ValueError, match=msg):
+        mstats.linregress(x, y)
+
+
+class TestTheilslopes:
+    def test_theilslopes(self):
+        # Test for basic slope and intercept.
+        slope, intercept, lower, upper = mstats.theilslopes([0, 1, 1])
+        assert_almost_equal(slope, 0.5)
+        assert_almost_equal(intercept, 0.5)
+
+        slope, intercept, lower, upper = mstats.theilslopes([0, 1, 1],
+                                                            method='joint')
+        assert_almost_equal(slope, 0.5)
+        assert_almost_equal(intercept, 0.0)
+
+        # Test for correct masking.
+        y = np.ma.array([0, 1, 100, 1], mask=[False, False, True, False])
+        slope, intercept, lower, upper = mstats.theilslopes(y)
+        assert_almost_equal(slope, 1./3)
+        assert_almost_equal(intercept, 2./3)
+
+        slope, intercept, lower, upper = mstats.theilslopes(y,
+                                                            method='joint')
+        assert_almost_equal(slope, 1./3)
+        assert_almost_equal(intercept, 0.0)
+
+        # Test of confidence intervals from example in Sen (1968).
+        x = [1, 2, 3, 4, 10, 12, 18]
+        y = [9, 15, 19, 20, 45, 55, 78]
+        slope, intercept, lower, upper = mstats.theilslopes(y, x, 0.07)
+        assert_almost_equal(slope, 4)
+        assert_almost_equal(intercept, 4.0)
+        assert_almost_equal(upper, 4.38, decimal=2)
+        assert_almost_equal(lower, 3.71, decimal=2)
+
+        slope, intercept, lower, upper = mstats.theilslopes(y, x, 0.07,
+                                                            method='joint')
+        assert_almost_equal(slope, 4)
+        assert_almost_equal(intercept, 6.0)
+        assert_almost_equal(upper, 4.38, decimal=2)
+        assert_almost_equal(lower, 3.71, decimal=2)
+
+
+    def test_theilslopes_warnings(self):
+        # Test `theilslopes` with degenerate input; see gh-15943
+        msg = "All `x` coordinates.*|Mean of empty slice.|invalid value encountered.*"
+        with pytest.warns(RuntimeWarning, match=msg):
+            res = mstats.theilslopes([0, 1], [0, 0])
+            assert np.all(np.isnan(res))
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, "invalid value encountered...")
+            res = mstats.theilslopes([0, 0, 0], [0, 1, 0])
+            assert_allclose(res, (0, 0, np.nan, np.nan))
+
+
+    def test_theilslopes_namedtuple_consistency(self):
+        """
+        Simple test to ensure tuple backwards-compatibility of the returned
+        TheilslopesResult object
+        """
+        y = [1, 2, 4]
+        x = [4, 6, 8]
+        slope, intercept, low_slope, high_slope = mstats.theilslopes(y, x)
+        result = mstats.theilslopes(y, x)
+
+        # note all four returned values are distinct here
+        assert_equal(slope, result.slope)
+        assert_equal(intercept, result.intercept)
+        assert_equal(low_slope, result.low_slope)
+        assert_equal(high_slope, result.high_slope)
+
+    def test_gh19678_uint8(self):
+        # `theilslopes` returned unexpected results when `y` was an unsigned type.
+        # Check that this is resolved.
+        rng = np.random.default_rng(2549824598234528)
+        y = rng.integers(0, 255, size=10, dtype=np.uint8)
+        res = stats.theilslopes(y, y)
+        np.testing.assert_allclose(res.slope, 1)
+
+
+def test_siegelslopes():
+    # method should be exact for straight line
+    y = 2 * np.arange(10) + 0.5
+    assert_equal(mstats.siegelslopes(y), (2.0, 0.5))
+    assert_equal(mstats.siegelslopes(y, method='separate'), (2.0, 0.5))
+
+    x = 2 * np.arange(10)
+    y = 5 * x - 3.0
+    assert_equal(mstats.siegelslopes(y, x), (5.0, -3.0))
+    assert_equal(mstats.siegelslopes(y, x, method='separate'), (5.0, -3.0))
+
+    # method is robust to outliers: brekdown point of 50%
+    y[:4] = 1000
+    assert_equal(mstats.siegelslopes(y, x), (5.0, -3.0))
+
+    # if there are no outliers, results should be comparble to linregress
+    x = np.arange(10)
+    y = -2.3 + 0.3*x + stats.norm.rvs(size=10, random_state=231)
+    slope_ols, intercept_ols, _, _, _ = stats.linregress(x, y)
+
+    slope, intercept = mstats.siegelslopes(y, x)
+    assert_allclose(slope, slope_ols, rtol=0.1)
+    assert_allclose(intercept, intercept_ols, rtol=0.1)
+
+    slope, intercept = mstats.siegelslopes(y, x, method='separate')
+    assert_allclose(slope, slope_ols, rtol=0.1)
+    assert_allclose(intercept, intercept_ols, rtol=0.1)
+
+
+def test_siegelslopes_namedtuple_consistency():
+    """
+    Simple test to ensure tuple backwards-compatibility of the returned
+    SiegelslopesResult object.
+    """
+    y = [1, 2, 4]
+    x = [4, 6, 8]
+    slope, intercept = mstats.siegelslopes(y, x)
+    result = mstats.siegelslopes(y, x)
+
+    # note both returned values are distinct here
+    assert_equal(slope, result.slope)
+    assert_equal(intercept, result.intercept)
+
+
+def test_sen_seasonal_slopes():
+    rng = np.random.default_rng(5765986256978575148)
+    x = rng.random(size=(100, 4))
+    intra_slope, inter_slope = mstats.sen_seasonal_slopes(x)
+
+    # reference implementation from the `sen_seasonal_slopes` documentation
+    def dijk(yi):
+        n = len(yi)
+        x = np.arange(n)
+        dy = yi - yi[:, np.newaxis]
+        dx = x - x[:, np.newaxis]
+        mask = np.triu(np.ones((n, n), dtype=bool), k=1)
+        return dy[mask]/dx[mask]
+
+    for i in range(4):
+        assert_allclose(np.median(dijk(x[:, i])), intra_slope[i])
+
+    all_slopes = np.concatenate([dijk(x[:, i]) for i in range(x.shape[1])])
+    assert_allclose(np.median(all_slopes), inter_slope)
+
+
+def test_plotting_positions():
+    # Regression test for #1256
+    pos = mstats.plotting_positions(np.arange(3), 0, 0)
+    assert_array_almost_equal(pos.data, np.array([0.25, 0.5, 0.75]))
+
+
+@skip_xp_invalid_arg
+class TestNormalitytests:
+
+    def test_vs_nonmasked(self):
+        x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
+        assert_array_almost_equal(mstats.normaltest(x),
+                                  stats.normaltest(x))
+        assert_array_almost_equal(mstats.skewtest(x),
+                                  stats.skewtest(x))
+        assert_array_almost_equal(mstats.kurtosistest(x),
+                                  stats.kurtosistest(x))
+
+        funcs = [stats.normaltest, stats.skewtest, stats.kurtosistest]
+        mfuncs = [mstats.normaltest, mstats.skewtest, mstats.kurtosistest]
+        x = [1, 2, 3, 4]
+        for func, mfunc in zip(funcs, mfuncs):
+            with pytest.warns(SmallSampleWarning, match=too_small_1d_not_omit):
+                res = func(x)
+                assert np.isnan(res.statistic)
+                assert np.isnan(res.pvalue)
+            assert_raises(ValueError, mfunc, x)
+
+    def test_axis_None(self):
+        # Test axis=None (equal to axis=0 for 1-D input)
+        x = np.array((-2,-1,0,1,2,3)*4)**2
+        assert_allclose(mstats.normaltest(x, axis=None), mstats.normaltest(x))
+        assert_allclose(mstats.skewtest(x, axis=None), mstats.skewtest(x))
+        assert_allclose(mstats.kurtosistest(x, axis=None),
+                        mstats.kurtosistest(x))
+
+    def test_maskedarray_input(self):
+        # Add some masked values, test result doesn't change
+        x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
+        xm = np.ma.array(np.r_[np.inf, x, 10],
+                         mask=np.r_[True, [False] * x.size, True])
+        assert_allclose(mstats.normaltest(xm), stats.normaltest(x))
+        assert_allclose(mstats.skewtest(xm), stats.skewtest(x))
+        assert_allclose(mstats.kurtosistest(xm), stats.kurtosistest(x))
+
+    def test_nd_input(self):
+        x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
+        x_2d = np.vstack([x] * 2).T
+        for func in [mstats.normaltest, mstats.skewtest, mstats.kurtosistest]:
+            res_1d = func(x)
+            res_2d = func(x_2d)
+            assert_allclose(res_2d[0], [res_1d[0]] * 2)
+            assert_allclose(res_2d[1], [res_1d[1]] * 2)
+
+    def test_normaltest_result_attributes(self):
+        x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
+        res = mstats.normaltest(x)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_kurtosistest_result_attributes(self):
+        x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
+        res = mstats.kurtosistest(x)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_regression_9033(self):
+        # x clearly non-normal but power of negative denom needs
+        # to be handled correctly to reject normality
+        counts = [128, 0, 58, 7, 0, 41, 16, 0, 0, 167]
+        x = np.hstack([np.full(c, i) for i, c in enumerate(counts)])
+        assert_equal(mstats.kurtosistest(x)[1] < 0.01, True)
+
+    @pytest.mark.parametrize("test", ["skewtest", "kurtosistest"])
+    @pytest.mark.parametrize("alternative", ["less", "greater"])
+    def test_alternative(self, test, alternative):
+        x = stats.norm.rvs(loc=10, scale=2.5, size=30, random_state=123)
+
+        stats_test = getattr(stats, test)
+        mstats_test = getattr(mstats, test)
+
+        z_ex, p_ex = stats_test(x, alternative=alternative)
+        z, p = mstats_test(x, alternative=alternative)
+        assert_allclose(z, z_ex, atol=1e-12)
+        assert_allclose(p, p_ex, atol=1e-12)
+
+        # test with masked arrays
+        x[1:5] = np.nan
+        x = np.ma.masked_array(x, mask=np.isnan(x))
+        z_ex, p_ex = stats_test(x.compressed(), alternative=alternative)
+        z, p = mstats_test(x, alternative=alternative)
+        assert_allclose(z, z_ex, atol=1e-12)
+        assert_allclose(p, p_ex, atol=1e-12)
+
+    def test_bad_alternative(self):
+        x = stats.norm.rvs(size=20, random_state=123)
+        msg = r"`alternative` must be..."
+
+        with pytest.raises(ValueError, match=msg):
+            mstats.skewtest(x, alternative='error')
+
+        with pytest.raises(ValueError, match=msg):
+            mstats.kurtosistest(x, alternative='error')
+
+
+class TestFOneway:
+    def test_result_attributes(self):
+        a = np.array([655, 788], dtype=np.uint16)
+        b = np.array([789, 772], dtype=np.uint16)
+        res = mstats.f_oneway(a, b)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+
+class TestMannwhitneyu:
+    # data from gh-1428
+    x = np.array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 2.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 2., 1., 1., 1., 1., 2., 1., 1., 2., 1., 1., 2.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 2., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 2., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 3., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1.])
+
+    y = np.array([1., 1., 1., 1., 1., 1., 1., 2., 1., 2., 1., 1., 1., 1.,
+                  2., 1., 1., 1., 2., 1., 1., 1., 1., 1., 2., 1., 1., 3.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 2., 1., 2., 1.,
+                  1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1., 2.,
+                  2., 1., 1., 2., 1., 1., 2., 1., 2., 1., 1., 1., 1., 2.,
+                  2., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  1., 2., 1., 1., 1., 1., 1., 2., 2., 2., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
+                  2., 1., 1., 2., 1., 1., 1., 1., 2., 1., 1., 1., 1., 1.,
+                  1., 1., 1., 1., 1., 1., 1., 2., 1., 1., 1., 2., 1., 1.,
+                  1., 1., 1., 1.])
+
+    def test_result_attributes(self):
+        res = mstats.mannwhitneyu(self.x, self.y)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_against_stats(self):
+        # gh-4641 reported that stats.mannwhitneyu returned half the p-value
+        # of mstats.mannwhitneyu. Default alternative of stats.mannwhitneyu
+        # is now two-sided, so they match.
+        res1 = mstats.mannwhitneyu(self.x, self.y)
+        res2 = stats.mannwhitneyu(self.x, self.y)
+        assert res1.statistic == res2.statistic
+        assert_allclose(res1.pvalue, res2.pvalue)
+
+
+class TestKruskal:
+    def test_result_attributes(self):
+        x = [1, 3, 5, 7, 9]
+        y = [2, 4, 6, 8, 10]
+
+        res = mstats.kruskal(x, y)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+
+# TODO: for all ttest functions, add tests with masked array inputs
+class TestTtest_rel:
+    def test_vs_nonmasked(self):
+        np.random.seed(1234567)
+        outcome = np.random.randn(20, 4) + [0, 0, 1, 2]
+
+        # 1-D inputs
+        res1 = stats.ttest_rel(outcome[:, 0], outcome[:, 1])
+        res2 = mstats.ttest_rel(outcome[:, 0], outcome[:, 1])
+        assert_allclose(res1, res2)
+
+        # 2-D inputs
+        res1 = stats.ttest_rel(outcome[:, 0], outcome[:, 1], axis=None)
+        res2 = mstats.ttest_rel(outcome[:, 0], outcome[:, 1], axis=None)
+        assert_allclose(res1, res2)
+        res1 = stats.ttest_rel(outcome[:, :2], outcome[:, 2:], axis=0)
+        res2 = mstats.ttest_rel(outcome[:, :2], outcome[:, 2:], axis=0)
+        assert_allclose(res1, res2)
+
+        # Check default is axis=0
+        res3 = mstats.ttest_rel(outcome[:, :2], outcome[:, 2:])
+        assert_allclose(res2, res3)
+
+    def test_fully_masked(self):
+        np.random.seed(1234567)
+        outcome = ma.masked_array(np.random.randn(3, 2),
+                                  mask=[[1, 1, 1], [0, 0, 0]])
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, "invalid value encountered in absolute")
+            for pair in [(outcome[:, 0], outcome[:, 1]),
+                         ([np.nan, np.nan], [1.0, 2.0])]:
+                t, p = mstats.ttest_rel(*pair)
+                assert_array_equal(t, (np.nan, np.nan))
+                assert_array_equal(p, (np.nan, np.nan))
+
+    def test_result_attributes(self):
+        np.random.seed(1234567)
+        outcome = np.random.randn(20, 4) + [0, 0, 1, 2]
+
+        res = mstats.ttest_rel(outcome[:, 0], outcome[:, 1])
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_invalid_input_size(self):
+        assert_raises(ValueError, mstats.ttest_rel,
+                      np.arange(10), np.arange(11))
+        x = np.arange(24)
+        assert_raises(ValueError, mstats.ttest_rel,
+                      x.reshape(2, 3, 4), x.reshape(2, 4, 3), axis=1)
+        assert_raises(ValueError, mstats.ttest_rel,
+                      x.reshape(2, 3, 4), x.reshape(2, 4, 3), axis=2)
+
+    def test_empty(self):
+        res1 = mstats.ttest_rel([], [])
+        assert_(np.all(np.isnan(res1)))
+
+    def test_zero_division(self):
+        t, p = mstats.ttest_ind([0, 0, 0], [1, 1, 1])
+        assert_equal((np.abs(t), p), (np.inf, 0))
+
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, "invalid value encountered in absolute")
+            t, p = mstats.ttest_ind([0, 0, 0], [0, 0, 0])
+            assert_array_equal(t, np.array([np.nan, np.nan]))
+            assert_array_equal(p, np.array([np.nan, np.nan]))
+
+    def test_bad_alternative(self):
+        msg = r"alternative must be 'less', 'greater' or 'two-sided'"
+        with pytest.raises(ValueError, match=msg):
+            mstats.ttest_ind([1, 2, 3], [4, 5, 6], alternative='foo')
+
+    @pytest.mark.parametrize("alternative", ["less", "greater"])
+    def test_alternative(self, alternative):
+        x = stats.norm.rvs(loc=10, scale=5, size=25, random_state=42)
+        y = stats.norm.rvs(loc=8, scale=2, size=25, random_state=42)
+
+        t_ex, p_ex = stats.ttest_rel(x, y, alternative=alternative)
+        t, p = mstats.ttest_rel(x, y, alternative=alternative)
+        assert_allclose(t, t_ex, rtol=1e-14)
+        assert_allclose(p, p_ex, rtol=1e-14)
+
+        # test with masked arrays
+        x[1:10] = np.nan
+        y[1:10] = np.nan
+        x = np.ma.masked_array(x, mask=np.isnan(x))
+        y = np.ma.masked_array(y, mask=np.isnan(y))
+        t, p = mstats.ttest_rel(x, y, alternative=alternative)
+        t_ex, p_ex = stats.ttest_rel(x.compressed(), y.compressed(),
+                                     alternative=alternative)
+        assert_allclose(t, t_ex, rtol=1e-14)
+        assert_allclose(p, p_ex, rtol=1e-14)
+
+
+class TestTtest_ind:
+    def test_vs_nonmasked(self):
+        np.random.seed(1234567)
+        outcome = np.random.randn(20, 4) + [0, 0, 1, 2]
+
+        # 1-D inputs
+        res1 = stats.ttest_ind(outcome[:, 0], outcome[:, 1])
+        res2 = mstats.ttest_ind(outcome[:, 0], outcome[:, 1])
+        assert_allclose(res1, res2)
+
+        # 2-D inputs
+        res1 = stats.ttest_ind(outcome[:, 0], outcome[:, 1], axis=None)
+        res2 = mstats.ttest_ind(outcome[:, 0], outcome[:, 1], axis=None)
+        assert_allclose(res1, res2)
+        res1 = stats.ttest_ind(outcome[:, :2], outcome[:, 2:], axis=0)
+        res2 = mstats.ttest_ind(outcome[:, :2], outcome[:, 2:], axis=0)
+        assert_allclose(res1, res2)
+
+        # Check default is axis=0
+        res3 = mstats.ttest_ind(outcome[:, :2], outcome[:, 2:])
+        assert_allclose(res2, res3)
+
+        # Check equal_var
+        res4 = stats.ttest_ind(outcome[:, 0], outcome[:, 1], equal_var=True)
+        res5 = mstats.ttest_ind(outcome[:, 0], outcome[:, 1], equal_var=True)
+        assert_allclose(res4, res5)
+        res4 = stats.ttest_ind(outcome[:, 0], outcome[:, 1], equal_var=False)
+        res5 = mstats.ttest_ind(outcome[:, 0], outcome[:, 1], equal_var=False)
+        assert_allclose(res4, res5)
+
+    def test_fully_masked(self):
+        np.random.seed(1234567)
+        outcome = ma.masked_array(np.random.randn(3, 2), mask=[[1, 1, 1], [0, 0, 0]])
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, "invalid value encountered in absolute")
+            for pair in [(outcome[:, 0], outcome[:, 1]),
+                         ([np.nan, np.nan], [1.0, 2.0])]:
+                t, p = mstats.ttest_ind(*pair)
+                assert_array_equal(t, (np.nan, np.nan))
+                assert_array_equal(p, (np.nan, np.nan))
+
+    def test_result_attributes(self):
+        np.random.seed(1234567)
+        outcome = np.random.randn(20, 4) + [0, 0, 1, 2]
+
+        res = mstats.ttest_ind(outcome[:, 0], outcome[:, 1])
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_empty(self):
+        res1 = mstats.ttest_ind([], [])
+        assert_(np.all(np.isnan(res1)))
+
+    def test_zero_division(self):
+        t, p = mstats.ttest_ind([0, 0, 0], [1, 1, 1])
+        assert_equal((np.abs(t), p), (np.inf, 0))
+
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, "invalid value encountered in absolute")
+            t, p = mstats.ttest_ind([0, 0, 0], [0, 0, 0])
+            assert_array_equal(t, (np.nan, np.nan))
+            assert_array_equal(p, (np.nan, np.nan))
+
+        t, p = mstats.ttest_ind([0, 0, 0], [1, 1, 1], equal_var=False)
+        assert_equal((np.abs(t), p), (np.inf, 0))
+        assert_array_equal(mstats.ttest_ind([0, 0, 0], [0, 0, 0],
+                                            equal_var=False), (np.nan, np.nan))
+
+    def test_bad_alternative(self):
+        msg = r"alternative must be 'less', 'greater' or 'two-sided'"
+        with pytest.raises(ValueError, match=msg):
+            mstats.ttest_ind([1, 2, 3], [4, 5, 6], alternative='foo')
+
+    @pytest.mark.parametrize("alternative", ["less", "greater"])
+    def test_alternative(self, alternative):
+        x = stats.norm.rvs(loc=10, scale=2, size=100, random_state=123)
+        y = stats.norm.rvs(loc=8, scale=2, size=100, random_state=123)
+
+        t_ex, p_ex = stats.ttest_ind(x, y, alternative=alternative)
+        t, p = mstats.ttest_ind(x, y, alternative=alternative)
+        assert_allclose(t, t_ex, rtol=1e-14)
+        assert_allclose(p, p_ex, rtol=1e-14)
+
+        # test with masked arrays
+        x[1:10] = np.nan
+        y[80:90] = np.nan
+        x = np.ma.masked_array(x, mask=np.isnan(x))
+        y = np.ma.masked_array(y, mask=np.isnan(y))
+        t_ex, p_ex = stats.ttest_ind(x.compressed(), y.compressed(),
+                                     alternative=alternative)
+        t, p = mstats.ttest_ind(x, y, alternative=alternative)
+        assert_allclose(t, t_ex, rtol=1e-14)
+        assert_allclose(p, p_ex, rtol=1e-14)
+
+
+class TestTtest_1samp:
+    def test_vs_nonmasked(self):
+        np.random.seed(1234567)
+        outcome = np.random.randn(20, 4) + [0, 0, 1, 2]
+
+        # 1-D inputs
+        res1 = stats.ttest_1samp(outcome[:, 0], 1)
+        res2 = mstats.ttest_1samp(outcome[:, 0], 1)
+        assert_allclose(res1, res2)
+
+    def test_fully_masked(self):
+        np.random.seed(1234567)
+        outcome = ma.masked_array(np.random.randn(3), mask=[1, 1, 1])
+        expected = (np.nan, np.nan)
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, "invalid value encountered in absolute")
+            for pair in [((np.nan, np.nan), 0.0), (outcome, 0.0)]:
+                t, p = mstats.ttest_1samp(*pair)
+                assert_array_equal(p, expected)
+                assert_array_equal(t, expected)
+
+    def test_result_attributes(self):
+        np.random.seed(1234567)
+        outcome = np.random.randn(20, 4) + [0, 0, 1, 2]
+
+        res = mstats.ttest_1samp(outcome[:, 0], 1)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_empty(self):
+        res1 = mstats.ttest_1samp([], 1)
+        assert_(np.all(np.isnan(res1)))
+
+    def test_zero_division(self):
+        t, p = mstats.ttest_1samp([0, 0, 0], 1)
+        assert_equal((np.abs(t), p), (np.inf, 0))
+
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, "invalid value encountered in absolute")
+            t, p = mstats.ttest_1samp([0, 0, 0], 0)
+            assert_(np.isnan(t))
+            assert_array_equal(p, (np.nan, np.nan))
+
+    def test_bad_alternative(self):
+        msg = r"alternative must be 'less', 'greater' or 'two-sided'"
+        with pytest.raises(ValueError, match=msg):
+            mstats.ttest_1samp([1, 2, 3], 4, alternative='foo')
+
+    @pytest.mark.parametrize("alternative", ["less", "greater"])
+    def test_alternative(self, alternative):
+        x = stats.norm.rvs(loc=10, scale=2, size=100, random_state=123)
+
+        t_ex, p_ex = stats.ttest_1samp(x, 9, alternative=alternative)
+        t, p = mstats.ttest_1samp(x, 9, alternative=alternative)
+        assert_allclose(t, t_ex, rtol=1e-14)
+        assert_allclose(p, p_ex, rtol=1e-14)
+
+        # test with masked arrays
+        x[1:10] = np.nan
+        x = np.ma.masked_array(x, mask=np.isnan(x))
+        t_ex, p_ex = stats.ttest_1samp(x.compressed(), 9,
+                                       alternative=alternative)
+        t, p = mstats.ttest_1samp(x, 9, alternative=alternative)
+        assert_allclose(t, t_ex, rtol=1e-14)
+        assert_allclose(p, p_ex, rtol=1e-14)
+
+
+class TestDescribe:
+    """
+    Tests for mstats.describe.
+
+    Note that there are also tests for `mstats.describe` in the
+    class TestCompareWithStats.
+    """
+    def test_basic_with_axis(self):
+        # This is a basic test that is also a regression test for gh-7303.
+        a = np.ma.masked_array([[0, 1, 2, 3, 4, 9],
+                                [5, 5, 0, 9, 3, 3]],
+                               mask=[[0, 0, 0, 0, 0, 1],
+                                     [0, 0, 1, 1, 0, 0]])
+        result = mstats.describe(a, axis=1)
+        assert_equal(result.nobs, [5, 4])
+        amin, amax = result.minmax
+        assert_equal(amin, [0, 3])
+        assert_equal(amax, [4, 5])
+        assert_equal(result.mean, [2.0, 4.0])
+        assert_equal(result.variance, [2.0, 1.0])
+        assert_equal(result.skewness, [0.0, 0.0])
+        assert_allclose(result.kurtosis, [-1.3, -2.0])
+
+
+@skip_xp_invalid_arg
+class TestCompareWithStats:
+    """
+    Class to compare mstats results with stats results.
+
+    It is in general assumed that scipy.stats is at a more mature stage than
+    stats.mstats.  If a routine in mstats results in similar results like in
+    scipy.stats, this is considered also as a proper validation of scipy.mstats
+    routine.
+
+    Different sample sizes are used for testing, as some problems between stats
+    and mstats are dependent on sample size.
+
+    Author: Alexander Loew
+
+    NOTE that some tests fail. This might be caused by
+    a) actual differences or bugs between stats and mstats
+    b) numerical inaccuracies
+    c) different definitions of routine interfaces
+
+    These failures need to be checked. Current workaround is to have disabled these
+    tests, but issuing reports on scipy-dev
+
+    """
+    def get_n(self):
+        """ Returns list of sample sizes to be used for comparison. """
+        return [1000, 100, 10, 5]
+
+    def generate_xy_sample(self, n):
+        # This routine generates numpy arrays and corresponding masked arrays
+        # with the same data, but additional masked values
+        np.random.seed(1234567)
+        x = np.random.randn(n)
+        y = x + np.random.randn(n)
+        xm = np.full(len(x) + 5, 1e16)
+        ym = np.full(len(y) + 5, 1e16)
+        xm[0:len(x)] = x
+        ym[0:len(y)] = y
+        mask = xm > 9e15
+        xm = np.ma.array(xm, mask=mask)
+        ym = np.ma.array(ym, mask=mask)
+        return x, y, xm, ym
+
+    def generate_xy_sample2D(self, n, nx):
+        x = np.full((n, nx), np.nan)
+        y = np.full((n, nx), np.nan)
+        xm = np.full((n+5, nx), np.nan)
+        ym = np.full((n+5, nx), np.nan)
+
+        for i in range(nx):
+            x[:, i], y[:, i], dx, dy = self.generate_xy_sample(n)
+
+        xm[0:n, :] = x[0:n]
+        ym[0:n, :] = y[0:n]
+        xm = np.ma.array(xm, mask=np.isnan(xm))
+        ym = np.ma.array(ym, mask=np.isnan(ym))
+        return x, y, xm, ym
+
+    def test_linregress(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            result1 = stats.linregress(x, y)
+            result2 = stats.mstats.linregress(xm, ym)
+            assert_allclose(np.asarray(result1), np.asarray(result2))
+
+    def test_pearsonr(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r, p = stats.pearsonr(x, y)
+            rm, pm = stats.mstats.pearsonr(xm, ym)
+
+            assert_almost_equal(r, rm, decimal=14)
+            assert_almost_equal(p, pm, decimal=14)
+
+    def test_spearmanr(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r, p = stats.spearmanr(x, y)
+            rm, pm = stats.mstats.spearmanr(xm, ym)
+            assert_almost_equal(r, rm, 14)
+            assert_almost_equal(p, pm, 14)
+
+    def test_spearmanr_backcompat_useties(self):
+        # A regression test to ensure we don't break backwards compat
+        # more than we have to (see gh-9204).
+        x = np.arange(6)
+        assert_raises(ValueError, mstats.spearmanr, x, x, False)
+
+    def test_gmean(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r = stats.gmean(abs(x))
+            rm = stats.mstats.gmean(abs(xm))
+            assert_allclose(r, rm, rtol=1e-13)
+
+            r = stats.gmean(abs(y))
+            rm = stats.mstats.gmean(abs(ym))
+            assert_allclose(r, rm, rtol=1e-13)
+
+    def test_hmean(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+
+            r = stats.hmean(abs(x))
+            rm = stats.mstats.hmean(abs(xm))
+            assert_almost_equal(r, rm, 10)
+
+            r = stats.hmean(abs(y))
+            rm = stats.mstats.hmean(abs(ym))
+            assert_almost_equal(r, rm, 10)
+
+    def test_skew(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+
+            r = stats.skew(x)
+            rm = stats.mstats.skew(xm)
+            assert_almost_equal(r, rm, 10)
+
+            r = stats.skew(y)
+            rm = stats.mstats.skew(ym)
+            assert_almost_equal(r, rm, 10)
+
+    def test_moment(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+
+            r = stats.moment(x)
+            rm = stats.mstats.moment(xm)
+            assert_almost_equal(r, rm, 10)
+
+            r = stats.moment(y)
+            rm = stats.mstats.moment(ym)
+            assert_almost_equal(r, rm, 10)
+
+    def test_zscore(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+
+            # reference solution
+            zx = (x - x.mean()) / x.std()
+            zy = (y - y.mean()) / y.std()
+
+            # validate stats
+            assert_allclose(stats.zscore(x), zx, rtol=1e-10)
+            assert_allclose(stats.zscore(y), zy, rtol=1e-10)
+
+            # compare stats and mstats
+            assert_allclose(stats.zscore(x), stats.mstats.zscore(xm[0:len(x)]),
+                            rtol=1e-10)
+            assert_allclose(stats.zscore(y), stats.mstats.zscore(ym[0:len(y)]),
+                            rtol=1e-10)
+
+    def test_kurtosis(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r = stats.kurtosis(x)
+            rm = stats.mstats.kurtosis(xm)
+            assert_almost_equal(r, rm, 10)
+
+            r = stats.kurtosis(y)
+            rm = stats.mstats.kurtosis(ym)
+            assert_almost_equal(r, rm, 10)
+
+    def test_sem(self):
+        # example from stats.sem doc
+        a = np.arange(20).reshape(5, 4)
+        am = np.ma.array(a)
+        r = stats.sem(a, ddof=1)
+        rm = stats.mstats.sem(am, ddof=1)
+
+        assert_allclose(r, 2.82842712, atol=1e-5)
+        assert_allclose(rm, 2.82842712, atol=1e-5)
+
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            assert_almost_equal(stats.mstats.sem(xm, axis=None, ddof=0),
+                                stats.sem(x, axis=None, ddof=0), decimal=13)
+            assert_almost_equal(stats.mstats.sem(ym, axis=None, ddof=0),
+                                stats.sem(y, axis=None, ddof=0), decimal=13)
+            assert_almost_equal(stats.mstats.sem(xm, axis=None, ddof=1),
+                                stats.sem(x, axis=None, ddof=1), decimal=13)
+            assert_almost_equal(stats.mstats.sem(ym, axis=None, ddof=1),
+                                stats.sem(y, axis=None, ddof=1), decimal=13)
+
+    def test_describe(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r = stats.describe(x, ddof=1)
+            rm = stats.mstats.describe(xm, ddof=1)
+            for ii in range(6):
+                assert_almost_equal(np.asarray(r[ii]),
+                                    np.asarray(rm[ii]),
+                                    decimal=12)
+
+    def test_describe_result_attributes(self):
+        actual = mstats.describe(np.arange(5))
+        attributes = ('nobs', 'minmax', 'mean', 'variance', 'skewness',
+                      'kurtosis')
+        check_named_results(actual, attributes, ma=True)
+
+    def test_rankdata(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r = stats.rankdata(x)
+            rm = stats.mstats.rankdata(x)
+            assert_allclose(r, rm)
+
+    def test_tmean(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            assert_almost_equal(stats.tmean(x),stats.mstats.tmean(xm), 14)
+            assert_almost_equal(stats.tmean(y),stats.mstats.tmean(ym), 14)
+
+    def test_tmax(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            assert_almost_equal(stats.tmax(x,2.),
+                                stats.mstats.tmax(xm,2.), 10)
+            assert_almost_equal(stats.tmax(y,2.),
+                                stats.mstats.tmax(ym,2.), 10)
+
+            assert_almost_equal(stats.tmax(x, upperlimit=3.),
+                                stats.mstats.tmax(xm, upperlimit=3.), 10)
+            assert_almost_equal(stats.tmax(y, upperlimit=3.),
+                                stats.mstats.tmax(ym, upperlimit=3.), 10)
+
+    def test_tmin(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            assert_equal(stats.tmin(x), stats.mstats.tmin(xm))
+            assert_equal(stats.tmin(y), stats.mstats.tmin(ym))
+
+            assert_almost_equal(stats.tmin(x, lowerlimit=-1.),
+                                stats.mstats.tmin(xm, lowerlimit=-1.), 10)
+            assert_almost_equal(stats.tmin(y, lowerlimit=-1.),
+                                stats.mstats.tmin(ym, lowerlimit=-1.), 10)
+
+    def test_zmap(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            z = stats.zmap(x, y)
+            zm = stats.mstats.zmap(xm, ym)
+            assert_allclose(z, zm[0:len(z)], atol=1e-10)
+
+    def test_variation(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            assert_almost_equal(stats.variation(x), stats.mstats.variation(xm),
+                                decimal=12)
+            assert_almost_equal(stats.variation(y), stats.mstats.variation(ym),
+                                decimal=12)
+
+    def test_tvar(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            assert_almost_equal(stats.tvar(x), stats.mstats.tvar(xm),
+                                decimal=12)
+            assert_almost_equal(stats.tvar(y), stats.mstats.tvar(ym),
+                                decimal=12)
+
+    def test_trimboth(self):
+        a = np.arange(20)
+        b = stats.trimboth(a, 0.1)
+        bm = stats.mstats.trimboth(a, 0.1)
+        assert_allclose(np.sort(b), bm.data[~bm.mask])
+
+    def test_tsem(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            assert_almost_equal(stats.tsem(x), stats.mstats.tsem(xm),
+                                decimal=14)
+            assert_almost_equal(stats.tsem(y), stats.mstats.tsem(ym),
+                                decimal=14)
+            assert_almost_equal(stats.tsem(x, limits=(-2., 2.)),
+                                stats.mstats.tsem(xm, limits=(-2., 2.)),
+                                decimal=14)
+
+    def test_skewtest(self):
+        # this test is for 1D data
+        for n in self.get_n():
+            if n > 8:
+                x, y, xm, ym = self.generate_xy_sample(n)
+                r = stats.skewtest(x)
+                rm = stats.mstats.skewtest(xm)
+                assert_allclose(r, rm)
+
+    def test_skewtest_result_attributes(self):
+        x = np.array((-2, -1, 0, 1, 2, 3)*4)**2
+        res = mstats.skewtest(x)
+        attributes = ('statistic', 'pvalue')
+        check_named_results(res, attributes, ma=True)
+
+    def test_skewtest_2D_notmasked(self):
+        # a normal ndarray is passed to the masked function
+        x = np.random.random((20, 2)) * 20.
+        r = stats.skewtest(x)
+        rm = stats.mstats.skewtest(x)
+        assert_allclose(np.asarray(r), np.asarray(rm))
+
+    def test_skewtest_2D_WithMask(self):
+        nx = 2
+        for n in self.get_n():
+            if n > 8:
+                x, y, xm, ym = self.generate_xy_sample2D(n, nx)
+                r = stats.skewtest(x)
+                rm = stats.mstats.skewtest(xm)
+
+                assert_allclose(r[0][0], rm[0][0], rtol=1e-14)
+                assert_allclose(r[0][1], rm[0][1], rtol=1e-14)
+
+    def test_normaltest(self):
+        with np.errstate(over='raise'), suppress_warnings() as sup:
+            sup.filter(UserWarning, "`kurtosistest` p-value may be inaccurate")
+            sup.filter(UserWarning, "kurtosistest only valid for n>=20")
+            for n in self.get_n():
+                if n > 8:
+                    x, y, xm, ym = self.generate_xy_sample(n)
+                    r = stats.normaltest(x)
+                    rm = stats.mstats.normaltest(xm)
+                    assert_allclose(np.asarray(r), np.asarray(rm))
+
+    def test_find_repeats(self):
+        x = np.asarray([1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4]).astype('float')
+        tmp = np.asarray([1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5]).astype('float')
+        mask = (tmp == 5.)
+        xm = np.ma.array(tmp, mask=mask)
+        x_orig, xm_orig = x.copy(), xm.copy()
+
+        r = stats.find_repeats(x)
+        rm = stats.mstats.find_repeats(xm)
+
+        assert_equal(r, rm)
+        assert_equal(x, x_orig)
+        assert_equal(xm, xm_orig)
+
+        # This crazy behavior is expected by count_tied_groups, but is not
+        # in the docstring...
+        _, counts = stats.mstats.find_repeats([])
+        assert_equal(counts, np.array(0, dtype=np.intp))
+
+    def test_kendalltau(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r = stats.kendalltau(x, y)
+            rm = stats.mstats.kendalltau(xm, ym)
+            assert_almost_equal(r[0], rm[0], decimal=10)
+            assert_almost_equal(r[1], rm[1], decimal=7)
+
+    def test_obrientransform(self):
+        for n in self.get_n():
+            x, y, xm, ym = self.generate_xy_sample(n)
+            r = stats.obrientransform(x)
+            rm = stats.mstats.obrientransform(xm)
+            assert_almost_equal(r.T, rm[0:len(x)])
+
+    def test_ks_1samp(self):
+        """Checks that mstats.ks_1samp and stats.ks_1samp agree on masked arrays."""
+        for mode in ['auto', 'exact', 'asymp']:
+            with suppress_warnings():
+                for alternative in ['less', 'greater', 'two-sided']:
+                    for n in self.get_n():
+                        x, y, xm, ym = self.generate_xy_sample(n)
+                        res1 = stats.ks_1samp(x, stats.norm.cdf,
+                                              alternative=alternative, mode=mode)
+                        res2 = stats.mstats.ks_1samp(xm, stats.norm.cdf,
+                                                     alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res2))
+                        res3 = stats.ks_1samp(xm, stats.norm.cdf,
+                                              alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res3))
+
+    def test_kstest_1samp(self):
+        """
+        Checks that 1-sample mstats.kstest and stats.kstest agree on masked arrays.
+        """
+        for mode in ['auto', 'exact', 'asymp']:
+            with suppress_warnings():
+                for alternative in ['less', 'greater', 'two-sided']:
+                    for n in self.get_n():
+                        x, y, xm, ym = self.generate_xy_sample(n)
+                        res1 = stats.kstest(x, 'norm',
+                                            alternative=alternative, mode=mode)
+                        res2 = stats.mstats.kstest(xm, 'norm',
+                                                   alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res2))
+                        res3 = stats.kstest(xm, 'norm',
+                                            alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res3))
+
+    def test_ks_2samp(self):
+        """Checks that mstats.ks_2samp and stats.ks_2samp agree on masked arrays.
+        gh-8431"""
+        for mode in ['auto', 'exact', 'asymp']:
+            with suppress_warnings() as sup:
+                if mode in ['auto', 'exact']:
+                    message = "ks_2samp: Exact calculation unsuccessful."
+                    sup.filter(RuntimeWarning, message)
+                for alternative in ['less', 'greater', 'two-sided']:
+                    for n in self.get_n():
+                        x, y, xm, ym = self.generate_xy_sample(n)
+                        res1 = stats.ks_2samp(x, y,
+                                              alternative=alternative, mode=mode)
+                        res2 = stats.mstats.ks_2samp(xm, ym,
+                                                     alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res2))
+                        res3 = stats.ks_2samp(xm, y,
+                                              alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res3))
+
+    def test_kstest_2samp(self):
+        """
+        Checks that 2-sample mstats.kstest and stats.kstest agree on masked arrays.
+        """
+        for mode in ['auto', 'exact', 'asymp']:
+            with suppress_warnings() as sup:
+                if mode in ['auto', 'exact']:
+                    message = "ks_2samp: Exact calculation unsuccessful."
+                    sup.filter(RuntimeWarning, message)
+                for alternative in ['less', 'greater', 'two-sided']:
+                    for n in self.get_n():
+                        x, y, xm, ym = self.generate_xy_sample(n)
+                        res1 = stats.kstest(x, y,
+                                            alternative=alternative, mode=mode)
+                        res2 = stats.mstats.kstest(xm, ym,
+                                                   alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res2))
+                        res3 = stats.kstest(xm, y,
+                                            alternative=alternative, mode=mode)
+                        assert_equal(np.asarray(res1), np.asarray(res3))
+
+
+class TestBrunnerMunzel:
+    # Data from (Lumley, 1996)
+    X = np.ma.masked_invalid([1, 2, 1, 1, 1, np.nan, 1, 1,
+                              1, 1, 1, 2, 4, 1, 1, np.nan])
+    Y = np.ma.masked_invalid([3, 3, 4, 3, np.nan, 1, 2, 3, 1, 1, 5, 4])
+    significant = 14
+
+    def test_brunnermunzel_one_sided(self):
+        # Results are compared with R's lawstat package.
+        u1, p1 = mstats.brunnermunzel(self.X, self.Y, alternative='less')
+        u2, p2 = mstats.brunnermunzel(self.Y, self.X, alternative='greater')
+        u3, p3 = mstats.brunnermunzel(self.X, self.Y, alternative='greater')
+        u4, p4 = mstats.brunnermunzel(self.Y, self.X, alternative='less')
+
+        assert_almost_equal(p1, p2, decimal=self.significant)
+        assert_almost_equal(p3, p4, decimal=self.significant)
+        assert_(p1 != p3)
+        assert_almost_equal(u1, 3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(u2, -3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(u3, 3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(u4, -3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(p1, 0.0028931043330757342,
+                            decimal=self.significant)
+        assert_almost_equal(p3, 0.99710689566692423,
+                            decimal=self.significant)
+
+    def test_brunnermunzel_two_sided(self):
+        # Results are compared with R's lawstat package.
+        u1, p1 = mstats.brunnermunzel(self.X, self.Y, alternative='two-sided')
+        u2, p2 = mstats.brunnermunzel(self.Y, self.X, alternative='two-sided')
+
+        assert_almost_equal(p1, p2, decimal=self.significant)
+        assert_almost_equal(u1, 3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(u2, -3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(p1, 0.0057862086661515377,
+                            decimal=self.significant)
+
+    def test_brunnermunzel_default(self):
+        # The default value for alternative is two-sided
+        u1, p1 = mstats.brunnermunzel(self.X, self.Y)
+        u2, p2 = mstats.brunnermunzel(self.Y, self.X)
+
+        assert_almost_equal(p1, p2, decimal=self.significant)
+        assert_almost_equal(u1, 3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(u2, -3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(p1, 0.0057862086661515377,
+                            decimal=self.significant)
+
+    def test_brunnermunzel_alternative_error(self):
+        alternative = "error"
+        distribution = "t"
+        assert_(alternative not in ["two-sided", "greater", "less"])
+        assert_raises(ValueError,
+                      mstats.brunnermunzel,
+                      self.X,
+                      self.Y,
+                      alternative,
+                      distribution)
+
+    def test_brunnermunzel_distribution_norm(self):
+        u1, p1 = mstats.brunnermunzel(self.X, self.Y, distribution="normal")
+        u2, p2 = mstats.brunnermunzel(self.Y, self.X, distribution="normal")
+        assert_almost_equal(p1, p2, decimal=self.significant)
+        assert_almost_equal(u1, 3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(u2, -3.1374674823029505,
+                            decimal=self.significant)
+        assert_almost_equal(p1, 0.0017041417600383024,
+                            decimal=self.significant)
+
+    def test_brunnermunzel_distribution_error(self):
+        alternative = "two-sided"
+        distribution = "error"
+        assert_(alternative not in ["t", "normal"])
+        assert_raises(ValueError,
+                      mstats.brunnermunzel,
+                      self.X,
+                      self.Y,
+                      alternative,
+                      distribution)
+
+    def test_brunnermunzel_empty_imput(self):
+        u1, p1 = mstats.brunnermunzel(self.X, [])
+        u2, p2 = mstats.brunnermunzel([], self.Y)
+        u3, p3 = mstats.brunnermunzel([], [])
+
+        assert_(np.isnan(u1))
+        assert_(np.isnan(p1))
+        assert_(np.isnan(u2))
+        assert_(np.isnan(p2))
+        assert_(np.isnan(u3))
+        assert_(np.isnan(p3))

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_multicomp.py

@@ -0,0 +1,404 @@
+import copy
+
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+
+from scipy import stats
+from scipy.stats._multicomp import _pvalue_dunnett, DunnettResult
+
+
+class TestDunnett:
+    # For the following tests, p-values were computed using Matlab, e.g.
+    #     sample = [18.  15.  18.  16.  17.  15.  14.  14.  14.  15.  15....
+    #               14.  15.  14.  22.  18.  21.  21.  10.  10.  11.  9....
+    #               25.  26.  17.5 16.  15.5 14.5 22.  22.  24.  22.5 29....
+    #               24.5 20.  18.  18.5 17.5 26.5 13.  16.5 13.  13.  13....
+    #               28.  27.  34.  31.  29.  27.  24.  23.  38.  36.  25....
+    #               38. 26.  22.  36.  27.  27.  32.  28.  31....
+    #               24.  27.  33.  32.  28.  19. 37.  31.  36.  36....
+    #               34.  38.  32.  38.  32....
+    #               26.  24.  26.  25.  29. 29.5 16.5 36.  44....
+    #               25.  27.  19....
+    #               25.  20....
+    #               28.];
+    #     j = [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...
+    #          0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...
+    #          0 0 0 0...
+    #          1 1 1 1 1 1 1 1 1 1 1 1 1 1 1...
+    #          2 2 2 2 2 2 2 2 2...
+    #          3 3 3...
+    #          4 4...
+    #          5];
+    #     [~, ~, stats] = anova1(sample, j, "off");
+    #     [results, ~, ~, gnames] = multcompare(stats, ...
+    #     "CriticalValueType", "dunnett", ...
+    #     "Approximate", false);
+    #     tbl = array2table(results, "VariableNames", ...
+    #     ["Group", "Control Group", "Lower Limit", ...
+    #     "Difference", "Upper Limit", "P-value"]);
+    #     tbl.("Group") = gnames(tbl.("Group"));
+    #     tbl.("Control Group") = gnames(tbl.("Control Group"))
+
+    # Matlab doesn't report the statistic, so the statistics were
+    # computed using R multcomp `glht`, e.g.:
+    #     library(multcomp)
+    #     options(digits=16)
+    #     control < - c(18.0, 15.0, 18.0, 16.0, 17.0, 15.0, 14.0, 14.0, 14.0,
+    #                   15.0, 15.0, 14.0, 15.0, 14.0, 22.0, 18.0, 21.0, 21.0,
+    #                   10.0, 10.0, 11.0, 9.0, 25.0, 26.0, 17.5, 16.0, 15.5,
+    #                   14.5, 22.0, 22.0, 24.0, 22.5, 29.0, 24.5, 20.0, 18.0,
+    #                   18.5, 17.5, 26.5, 13.0, 16.5, 13.0, 13.0, 13.0, 28.0,
+    #                   27.0, 34.0, 31.0, 29.0, 27.0, 24.0, 23.0, 38.0, 36.0,
+    #                   25.0, 38.0, 26.0, 22.0, 36.0, 27.0, 27.0, 32.0, 28.0,
+    #                   31.0)
+    #     t < - c(24.0, 27.0, 33.0, 32.0, 28.0, 19.0, 37.0, 31.0, 36.0, 36.0,
+    #             34.0, 38.0, 32.0, 38.0, 32.0)
+    #     w < - c(26.0, 24.0, 26.0, 25.0, 29.0, 29.5, 16.5, 36.0, 44.0)
+    #     x < - c(25.0, 27.0, 19.0)
+    #     y < - c(25.0, 20.0)
+    #     z < - c(28.0)
+    #
+    #     groups = factor(rep(c("control", "t", "w", "x", "y", "z"),
+    #                         times=c(length(control), length(t), length(w),
+    #                                 length(x), length(y), length(z))))
+    #     df < - data.frame(response=c(control, t, w, x, y, z),
+    #                       group=groups)
+    #     model < - aov(response
+    #     ~group, data = df)
+    #     test < - glht(model=model,
+    #                   linfct=mcp(group="Dunnett"),
+    #                   alternative="g")
+    #     summary(test)
+    #     confint(test)
+    # p-values agreed with those produced by Matlab to at least atol=1e-3
+
+    # From Matlab's documentation on multcompare
+    samples_1 = [
+        [
+            24.0, 27.0, 33.0, 32.0, 28.0, 19.0, 37.0, 31.0, 36.0, 36.0,
+            34.0, 38.0, 32.0, 38.0, 32.0
+        ],
+        [26.0, 24.0, 26.0, 25.0, 29.0, 29.5, 16.5, 36.0, 44.0],
+        [25.0, 27.0, 19.0],
+        [25.0, 20.0],
+        [28.0]
+    ]
+    control_1 = [
+        18.0, 15.0, 18.0, 16.0, 17.0, 15.0, 14.0, 14.0, 14.0, 15.0, 15.0,
+        14.0, 15.0, 14.0, 22.0, 18.0, 21.0, 21.0, 10.0, 10.0, 11.0, 9.0,
+        25.0, 26.0, 17.5, 16.0, 15.5, 14.5, 22.0, 22.0, 24.0, 22.5, 29.0,
+        24.5, 20.0, 18.0, 18.5, 17.5, 26.5, 13.0, 16.5, 13.0, 13.0, 13.0,
+        28.0, 27.0, 34.0, 31.0, 29.0, 27.0, 24.0, 23.0, 38.0, 36.0, 25.0,
+        38.0, 26.0, 22.0, 36.0, 27.0, 27.0, 32.0, 28.0, 31.0
+    ]
+    pvalue_1 = [4.727e-06, 0.022346, 0.97912, 0.99953, 0.86579]  # Matlab
+    # Statistic, alternative p-values, and CIs computed with R multcomp `glht`
+    p_1_twosided = [1e-4, 0.02237, 0.97913, 0.99953, 0.86583]
+    p_1_greater = [1e-4, 0.011217, 0.768500, 0.896991, 0.577211]
+    p_1_less = [1, 1, 0.99660, 0.98398, .99953]
+    statistic_1 = [5.27356, 2.91270, 0.60831, 0.27002, 0.96637]
+    ci_1_twosided = [[5.3633917835622, 0.7296142201217, -8.3879817106607,
+                      -11.9090753452911, -11.7655021543469],
+                     [15.9709832164378, 13.8936496687672, 13.4556900439941,
+                      14.6434503452911, 25.4998771543469]]
+    ci_1_greater = [5.9036402398526, 1.4000632918725, -7.2754756323636,
+                    -10.5567456382391, -9.8675629499576]
+    ci_1_less = [15.4306165948619, 13.2230539537359, 12.3429406339544,
+                 13.2908248513211, 23.6015228251660]
+    pvalues_1 = dict(twosided=p_1_twosided, less=p_1_less, greater=p_1_greater)
+    cis_1 = dict(twosided=ci_1_twosided, less=ci_1_less, greater=ci_1_greater)
+    case_1 = dict(samples=samples_1, control=control_1, statistic=statistic_1,
+                  pvalues=pvalues_1, cis=cis_1)
+
+    # From Dunnett1955 comparing with R's DescTools: DunnettTest
+    samples_2 = [[9.76, 8.80, 7.68, 9.36], [12.80, 9.68, 12.16, 9.20, 10.55]]
+    control_2 = [7.40, 8.50, 7.20, 8.24, 9.84, 8.32]
+    pvalue_2 = [0.6201, 0.0058]
+    # Statistic, alternative p-values, and CIs computed with R multcomp `glht`
+    p_2_twosided = [0.6201020, 0.0058254]
+    p_2_greater = [0.3249776, 0.0029139]
+    p_2_less = [0.91676, 0.99984]
+    statistic_2 = [0.85703, 3.69375]
+    ci_2_twosided = [[-1.2564116462124, 0.8396273539789],
+                     [2.5564116462124, 4.4163726460211]]
+    ci_2_greater = [-0.9588591188156, 1.1187563667543]
+    ci_2_less = [2.2588591188156, 4.1372436332457]
+    pvalues_2 = dict(twosided=p_2_twosided, less=p_2_less, greater=p_2_greater)
+    cis_2 = dict(twosided=ci_2_twosided, less=ci_2_less, greater=ci_2_greater)
+    case_2 = dict(samples=samples_2, control=control_2, statistic=statistic_2,
+                  pvalues=pvalues_2, cis=cis_2)
+
+    samples_3 = [[55, 64, 64], [55, 49, 52], [50, 44, 41]]
+    control_3 = [55, 47, 48]
+    pvalue_3 = [0.0364, 0.8966, 0.4091]
+    # Statistic, alternative p-values, and CIs computed with R multcomp `glht`
+    p_3_twosided = [0.036407, 0.896539, 0.409295]
+    p_3_greater = [0.018277, 0.521109, 0.981892]
+    p_3_less = [0.99944, 0.90054, 0.20974]
+    statistic_3 = [3.09073, 0.56195, -1.40488]
+    ci_3_twosided = [[0.7529028025053, -8.2470971974947, -15.2470971974947],
+                     [21.2470971974947, 12.2470971974947, 5.2470971974947]]
+    ci_3_greater = [2.4023682323149, -6.5976317676851, -13.5976317676851]
+    ci_3_less = [19.5984402363662, 10.5984402363662, 3.5984402363662]
+    pvalues_3 = dict(twosided=p_3_twosided, less=p_3_less, greater=p_3_greater)
+    cis_3 = dict(twosided=ci_3_twosided, less=ci_3_less, greater=ci_3_greater)
+    case_3 = dict(samples=samples_3, control=control_3, statistic=statistic_3,
+                  pvalues=pvalues_3, cis=cis_3)
+
+    # From Thomson and Short,
+    # Mucociliary function in health, chronic obstructive airway disease,
+    # and asbestosis, Journal of Applied Physiology, 1969. Table 1
+    # Comparing with R's DescTools: DunnettTest
+    samples_4 = [[3.8, 2.7, 4.0, 2.4], [2.8, 3.4, 3.7, 2.2, 2.0]]
+    control_4 = [2.9, 3.0, 2.5, 2.6, 3.2]
+    pvalue_4 = [0.5832, 0.9982]
+    # Statistic, alternative p-values, and CIs computed with R multcomp `glht`
+    p_4_twosided = [0.58317, 0.99819]
+    p_4_greater = [0.30225, 0.69115]
+    p_4_less = [0.91929, 0.65212]
+    statistic_4 = [0.90875, -0.05007]
+    ci_4_twosided = [[-0.6898153448579, -1.0333456251632],
+                     [1.4598153448579, 0.9933456251632]]
+    ci_4_greater = [-0.5186459268412, -0.8719655502147 ]
+    ci_4_less = [1.2886459268412, 0.8319655502147]
+    pvalues_4 = dict(twosided=p_4_twosided, less=p_4_less, greater=p_4_greater)
+    cis_4 = dict(twosided=ci_4_twosided, less=ci_4_less, greater=ci_4_greater)
+    case_4 = dict(samples=samples_4, control=control_4, statistic=statistic_4,
+                  pvalues=pvalues_4, cis=cis_4)
+
+    @pytest.mark.parametrize(
+        'rho, n_groups, df, statistic, pvalue, alternative',
+        [
+            # From Dunnett1955
+            # Tables 1a and 1b pages 1117-1118
+            (0.5, 1, 10, 1.81, 0.05, "greater"),  # different than two-sided
+            (0.5, 3, 10, 2.34, 0.05, "greater"),
+            (0.5, 2, 30, 1.99, 0.05, "greater"),
+            (0.5, 5, 30, 2.33, 0.05, "greater"),
+            (0.5, 4, 12, 3.32, 0.01, "greater"),
+            (0.5, 7, 12, 3.56, 0.01, "greater"),
+            (0.5, 2, 60, 2.64, 0.01, "greater"),
+            (0.5, 4, 60, 2.87, 0.01, "greater"),
+            (0.5, 4, 60, [2.87, 2.21], [0.01, 0.05], "greater"),
+            # Tables 2a and 2b pages 1119-1120
+            (0.5, 1, 10, 2.23, 0.05, "two-sided"),  # two-sided
+            (0.5, 3, 10, 2.81, 0.05, "two-sided"),
+            (0.5, 2, 30, 2.32, 0.05, "two-sided"),
+            (0.5, 3, 20, 2.57, 0.05, "two-sided"),
+            (0.5, 4, 12, 3.76, 0.01, "two-sided"),
+            (0.5, 7, 12, 4.08, 0.01, "two-sided"),
+            (0.5, 2, 60, 2.90, 0.01, "two-sided"),
+            (0.5, 4, 60, 3.14, 0.01, "two-sided"),
+            (0.5, 4, 60, [3.14, 2.55], [0.01, 0.05], "two-sided"),
+        ],
+    )
+    def test_critical_values(
+        self, rho, n_groups, df, statistic, pvalue, alternative
+    ):
+        rng = np.random.default_rng(165250594791731684851746311027739134893)
+        rho = np.full((n_groups, n_groups), rho)
+        np.fill_diagonal(rho, 1)
+
+        statistic = np.array(statistic)
+        res = _pvalue_dunnett(
+            rho=rho, df=df, statistic=statistic,
+            alternative=alternative,
+            rng=rng
+        )
+        assert_allclose(res, pvalue, atol=5e-3)
+
+    @pytest.mark.parametrize(
+        'samples, control, pvalue, statistic',
+        [
+            (samples_1, control_1, pvalue_1, statistic_1),
+            (samples_2, control_2, pvalue_2, statistic_2),
+            (samples_3, control_3, pvalue_3, statistic_3),
+            (samples_4, control_4, pvalue_4, statistic_4),
+        ]
+    )
+    def test_basic(self, samples, control, pvalue, statistic):
+        rng = np.random.default_rng(11681140010308601919115036826969764808)
+
+        res = stats.dunnett(*samples, control=control, random_state=rng)
+
+        assert isinstance(res, DunnettResult)
+        assert_allclose(res.statistic, statistic, rtol=5e-5)
+        assert_allclose(res.pvalue, pvalue, rtol=1e-2, atol=1e-4)
+
+    @pytest.mark.parametrize(
+        'alternative',
+        ['two-sided', 'less', 'greater']
+    )
+    def test_ttest_ind(self, alternative):
+        # check that `dunnett` agrees with `ttest_ind`
+        # when there are only two groups
+        rng = np.random.default_rng(114184017807316971636137493526995620351)
+
+        for _ in range(10):
+            sample = rng.integers(-100, 100, size=(10,))
+            control = rng.integers(-100, 100, size=(10,))
+
+            res = stats.dunnett(
+                sample, control=control,
+                alternative=alternative, random_state=rng
+            )
+            ref = stats.ttest_ind(
+                sample, control,
+                alternative=alternative, random_state=rng
+            )
+
+            assert_allclose(res.statistic, ref.statistic, rtol=1e-3, atol=1e-5)
+            assert_allclose(res.pvalue, ref.pvalue, rtol=1e-3, atol=1e-5)
+
+    @pytest.mark.parametrize(
+        'alternative, pvalue',
+        [
+            ('less', [0, 1]),
+            ('greater', [1, 0]),
+            ('two-sided', [0, 0]),
+        ]
+    )
+    def test_alternatives(self, alternative, pvalue):
+        rng = np.random.default_rng(114184017807316971636137493526995620351)
+
+        # width of 20 and min diff between samples/control is 60
+        # and maximal diff would be 100
+        sample_less = rng.integers(0, 20, size=(10,))
+        control = rng.integers(80, 100, size=(10,))
+        sample_greater = rng.integers(160, 180, size=(10,))
+
+        res = stats.dunnett(
+            sample_less, sample_greater, control=control,
+            alternative=alternative, random_state=rng
+        )
+        assert_allclose(res.pvalue, pvalue, atol=1e-7)
+
+        ci = res.confidence_interval()
+        # two-sided is comparable for high/low
+        if alternative == 'less':
+            assert np.isneginf(ci.low).all()
+            assert -100 < ci.high[0] < -60
+            assert 60 < ci.high[1] < 100
+        elif alternative == 'greater':
+            assert -100 < ci.low[0] < -60
+            assert 60 < ci.low[1] < 100
+            assert np.isposinf(ci.high).all()
+        elif alternative == 'two-sided':
+            assert -100 < ci.low[0] < -60
+            assert 60 < ci.low[1] < 100
+            assert -100 < ci.high[0] < -60
+            assert 60 < ci.high[1] < 100
+
+    @pytest.mark.parametrize("case", [case_1, case_2, case_3, case_4])
+    @pytest.mark.parametrize("alternative", ['less', 'greater', 'two-sided'])
+    def test_against_R_multicomp_glht(self, case, alternative):
+        rng = np.random.default_rng(189117774084579816190295271136455278291)
+        samples = case['samples']
+        control = case['control']
+        alternatives = {'less': 'less', 'greater': 'greater',
+                        'two-sided': 'twosided'}
+        p_ref = case['pvalues'][alternative.replace('-', '')]
+
+        res = stats.dunnett(*samples, control=control, alternative=alternative,
+                            random_state=rng)
+        # atol can't be tighter because R reports some pvalues as "< 1e-4"
+        assert_allclose(res.pvalue, p_ref, rtol=5e-3, atol=1e-4)
+
+        ci_ref = case['cis'][alternatives[alternative]]
+        if alternative == "greater":
+            ci_ref = [ci_ref, np.inf]
+        elif alternative == "less":
+            ci_ref = [-np.inf, ci_ref]
+        assert res._ci is None
+        assert res._ci_cl is None
+        ci = res.confidence_interval(confidence_level=0.95)
+        assert_allclose(ci.low, ci_ref[0], rtol=5e-3, atol=1e-5)
+        assert_allclose(ci.high, ci_ref[1], rtol=5e-3, atol=1e-5)
+
+        # re-run to use the cached value "is" to check id as same object
+        assert res._ci is ci
+        assert res._ci_cl == 0.95
+        ci_ = res.confidence_interval(confidence_level=0.95)
+        assert ci_ is ci
+
+    @pytest.mark.parametrize('alternative', ["two-sided", "less", "greater"])
+    def test_str(self, alternative):
+        rng = np.random.default_rng(189117774084579816190295271136455278291)
+
+        res = stats.dunnett(
+            *self.samples_3, control=self.control_3, alternative=alternative,
+            random_state=rng
+        )
+
+        # check some str output
+        res_str = str(res)
+        assert '(Sample 2 - Control)' in res_str
+        assert '95.0%' in res_str
+
+        if alternative == 'less':
+            assert '-inf' in res_str
+            assert '19.' in res_str
+        elif alternative == 'greater':
+            assert 'inf' in res_str
+            assert '-13.' in res_str
+        else:
+            assert 'inf' not in res_str
+            assert '21.' in res_str
+
+    def test_warnings(self):
+        rng = np.random.default_rng(189117774084579816190295271136455278291)
+
+        res = stats.dunnett(
+            *self.samples_3, control=self.control_3, random_state=rng
+        )
+        msg = r"Computation of the confidence interval did not converge"
+        with pytest.warns(UserWarning, match=msg):
+            res._allowance(tol=1e-5)
+
+    def test_raises(self):
+        samples, control = self.samples_3, self.control_3
+
+        # alternative
+        with pytest.raises(ValueError, match="alternative must be"):
+            stats.dunnett(*samples, control=control, alternative='bob')
+
+        # 2D for a sample
+        samples_ = copy.deepcopy(samples)
+        samples_[0] = [samples_[0]]
+        with pytest.raises(ValueError, match="must be 1D arrays"):
+            stats.dunnett(*samples_, control=control)
+
+        # 2D for control
+        control_ = copy.deepcopy(control)
+        control_ = [control_]
+        with pytest.raises(ValueError, match="must be 1D arrays"):
+            stats.dunnett(*samples, control=control_)
+
+        # No obs in a sample
+        samples_ = copy.deepcopy(samples)
+        samples_[1] = []
+        with pytest.raises(ValueError, match="at least 1 observation"):
+            stats.dunnett(*samples_, control=control)
+
+        # No obs in control
+        control_ = []
+        with pytest.raises(ValueError, match="at least 1 observation"):
+            stats.dunnett(*samples, control=control_)
+
+        res = stats.dunnett(*samples, control=control)
+        with pytest.raises(ValueError, match="Confidence level must"):
+            res.confidence_interval(confidence_level=3)
+
+    @pytest.mark.filterwarnings("ignore:Computation of the confidence")
+    @pytest.mark.parametrize('n_samples', [1, 2, 3])
+    def test_shapes(self, n_samples):
+        rng = np.random.default_rng(689448934110805334)
+        samples = rng.normal(size=(n_samples, 10))
+        control = rng.normal(size=10)
+        res = stats.dunnett(*samples, control=control, random_state=rng)
+        assert res.statistic.shape == (n_samples,)
+        assert res.pvalue.shape == (n_samples,)
+        ci = res.confidence_interval()
+        assert ci.low.shape == (n_samples,)
+        assert ci.high.shape == (n_samples,)

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_odds_ratio.py

@@ -0,0 +1,148 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+from .._discrete_distns import nchypergeom_fisher, hypergeom
+from scipy.stats._odds_ratio import odds_ratio
+from .data.fisher_exact_results_from_r import data
+
+
+class TestOddsRatio:
+
+    @pytest.mark.parametrize('parameters, rresult', data)
+    def test_results_from_r(self, parameters, rresult):
+        alternative = parameters.alternative.replace('.', '-')
+        result = odds_ratio(parameters.table)
+        # The results computed by R are not very accurate.
+        if result.statistic < 400:
+            or_rtol = 5e-4
+            ci_rtol = 2e-2
+        else:
+            or_rtol = 5e-2
+            ci_rtol = 1e-1
+        assert_allclose(result.statistic,
+                        rresult.conditional_odds_ratio, rtol=or_rtol)
+        ci = result.confidence_interval(parameters.confidence_level,
+                                        alternative)
+        assert_allclose((ci.low, ci.high), rresult.conditional_odds_ratio_ci,
+                        rtol=ci_rtol)
+
+        # Also do a self-check for the conditional odds ratio.
+        # With the computed conditional odds ratio as the noncentrality
+        # parameter of the noncentral hypergeometric distribution with
+        # parameters table.sum(), table[0].sum(), and table[:,0].sum() as
+        # total, ngood and nsample, respectively, the mean of the distribution
+        # should equal table[0, 0].
+        cor = result.statistic
+        table = np.array(parameters.table)
+        total = table.sum()
+        ngood = table[0].sum()
+        nsample = table[:, 0].sum()
+        # nchypergeom_fisher does not allow the edge cases where the
+        # noncentrality parameter is 0 or inf, so handle those values
+        # separately here.
+        if cor == 0:
+            nchg_mean = hypergeom.support(total, ngood, nsample)[0]
+        elif cor == np.inf:
+            nchg_mean = hypergeom.support(total, ngood, nsample)[1]
+        else:
+            nchg_mean = nchypergeom_fisher.mean(total, ngood, nsample, cor)
+        assert_allclose(nchg_mean, table[0, 0], rtol=1e-13)
+
+        # Check that the confidence interval is correct.
+        alpha = 1 - parameters.confidence_level
+        if alternative == 'two-sided':
+            if ci.low > 0:
+                sf = nchypergeom_fisher.sf(table[0, 0] - 1,
+                                           total, ngood, nsample, ci.low)
+                assert_allclose(sf, alpha/2, rtol=1e-11)
+            if np.isfinite(ci.high):
+                cdf = nchypergeom_fisher.cdf(table[0, 0],
+                                             total, ngood, nsample, ci.high)
+                assert_allclose(cdf, alpha/2, rtol=1e-11)
+        elif alternative == 'less':
+            if np.isfinite(ci.high):
+                cdf = nchypergeom_fisher.cdf(table[0, 0],
+                                             total, ngood, nsample, ci.high)
+                assert_allclose(cdf, alpha, rtol=1e-11)
+        else:
+            # alternative == 'greater'
+            if ci.low > 0:
+                sf = nchypergeom_fisher.sf(table[0, 0] - 1,
+                                           total, ngood, nsample, ci.low)
+                assert_allclose(sf, alpha, rtol=1e-11)
+
+    @pytest.mark.parametrize('table', [
+        [[0, 0], [5, 10]],
+        [[5, 10], [0, 0]],
+        [[0, 5], [0, 10]],
+        [[5, 0], [10, 0]],
+    ])
+    def test_row_or_col_zero(self, table):
+        result = odds_ratio(table)
+        assert_equal(result.statistic, np.nan)
+        ci = result.confidence_interval()
+        assert_equal((ci.low, ci.high), (0, np.inf))
+
+    @pytest.mark.parametrize("case",
+                             [[0.95, 'two-sided', 0.4879913, 2.635883],
+                              [0.90, 'two-sided', 0.5588516, 2.301663]])
+    def test_sample_odds_ratio_ci(self, case):
+        # Compare the sample odds ratio confidence interval to the R function
+        # oddsratio.wald from the epitools package, e.g.
+        # > library(epitools)
+        # > table = matrix(c(10, 20, 41, 93), nrow=2, ncol=2, byrow=TRUE)
+        # > result = oddsratio.wald(table)
+        # > result$measure
+        #           odds ratio with 95% C.I.
+        # Predictor  estimate     lower    upper
+        #   Exposed1 1.000000        NA       NA
+        #   Exposed2 1.134146 0.4879913 2.635883
+
+        confidence_level, alternative, ref_low, ref_high = case
+        table = [[10, 20], [41, 93]]
+        result = odds_ratio(table, kind='sample')
+        assert_allclose(result.statistic, 1.134146, rtol=1e-6)
+        ci = result.confidence_interval(confidence_level, alternative)
+        assert_allclose([ci.low, ci.high], [ref_low, ref_high], rtol=1e-6)
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize('alternative', ['less', 'greater', 'two-sided'])
+    def test_sample_odds_ratio_one_sided_ci(self, alternative):
+        # can't find a good reference for one-sided CI, so bump up the sample
+        # size and compare against the conditional odds ratio CI
+        table = [[1000, 2000], [4100, 9300]]
+        res = odds_ratio(table, kind='sample')
+        ref = odds_ratio(table, kind='conditional')
+        assert_allclose(res.statistic, ref.statistic, atol=1e-5)
+        assert_allclose(res.confidence_interval(alternative=alternative),
+                        ref.confidence_interval(alternative=alternative),
+                        atol=2e-3)
+
+    @pytest.mark.parametrize('kind', ['sample', 'conditional'])
+    @pytest.mark.parametrize('bad_table', [123, "foo", [10, 11, 12]])
+    def test_invalid_table_shape(self, kind, bad_table):
+        with pytest.raises(ValueError, match="Invalid shape"):
+            odds_ratio(bad_table, kind=kind)
+
+    def test_invalid_table_type(self):
+        with pytest.raises(ValueError, match='must be an array of integers'):
+            odds_ratio([[1.0, 3.4], [5.0, 9.9]])
+
+    def test_negative_table_values(self):
+        with pytest.raises(ValueError, match='must be nonnegative'):
+            odds_ratio([[1, 2], [3, -4]])
+
+    def test_invalid_kind(self):
+        with pytest.raises(ValueError, match='`kind` must be'):
+            odds_ratio([[10, 20], [30, 14]], kind='magnetoreluctance')
+
+    def test_invalid_alternative(self):
+        result = odds_ratio([[5, 10], [2, 32]])
+        with pytest.raises(ValueError, match='`alternative` must be'):
+            result.confidence_interval(alternative='depleneration')
+
+    @pytest.mark.parametrize('level', [-0.5, 1.5])
+    def test_invalid_confidence_level(self, level):
+        result = odds_ratio([[5, 10], [2, 32]])
+        with pytest.raises(ValueError, match='must be between 0 and 1'):
+            result.confidence_interval(confidence_level=level)

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_rank.py

@@ -0,0 +1,338 @@
+import numpy as np
+from numpy.testing import assert_equal, assert_array_equal
+import pytest
+
+from scipy.conftest import skip_xp_invalid_arg
+from scipy.stats import rankdata, tiecorrect
+from scipy._lib._util import np_long
+
+
+class TestTieCorrect:
+
+    def test_empty(self):
+        """An empty array requires no correction, should return 1.0."""
+        ranks = np.array([], dtype=np.float64)
+        c = tiecorrect(ranks)
+        assert_equal(c, 1.0)
+
+    def test_one(self):
+        """A single element requires no correction, should return 1.0."""
+        ranks = np.array([1.0], dtype=np.float64)
+        c = tiecorrect(ranks)
+        assert_equal(c, 1.0)
+
+    def test_no_correction(self):
+        """Arrays with no ties require no correction."""
+        ranks = np.arange(2.0)
+        c = tiecorrect(ranks)
+        assert_equal(c, 1.0)
+        ranks = np.arange(3.0)
+        c = tiecorrect(ranks)
+        assert_equal(c, 1.0)
+
+    def test_basic(self):
+        """Check a few basic examples of the tie correction factor."""
+        # One tie of two elements
+        ranks = np.array([1.0, 2.5, 2.5])
+        c = tiecorrect(ranks)
+        T = 2.0
+        N = ranks.size
+        expected = 1.0 - (T**3 - T) / (N**3 - N)
+        assert_equal(c, expected)
+
+        # One tie of two elements (same as above, but tie is not at the end)
+        ranks = np.array([1.5, 1.5, 3.0])
+        c = tiecorrect(ranks)
+        T = 2.0
+        N = ranks.size
+        expected = 1.0 - (T**3 - T) / (N**3 - N)
+        assert_equal(c, expected)
+
+        # One tie of three elements
+        ranks = np.array([1.0, 3.0, 3.0, 3.0])
+        c = tiecorrect(ranks)
+        T = 3.0
+        N = ranks.size
+        expected = 1.0 - (T**3 - T) / (N**3 - N)
+        assert_equal(c, expected)
+
+        # Two ties, lengths 2 and 3.
+        ranks = np.array([1.5, 1.5, 4.0, 4.0, 4.0])
+        c = tiecorrect(ranks)
+        T1 = 2.0
+        T2 = 3.0
+        N = ranks.size
+        expected = 1.0 - ((T1**3 - T1) + (T2**3 - T2)) / (N**3 - N)
+        assert_equal(c, expected)
+
+    def test_overflow(self):
+        ntie, k = 2000, 5
+        a = np.repeat(np.arange(k), ntie)
+        n = a.size  # ntie * k
+        out = tiecorrect(rankdata(a))
+        assert_equal(out, 1.0 - k * (ntie**3 - ntie) / float(n**3 - n))
+
+
+class TestRankData:
+
+    def test_empty(self):
+        """stats.rankdata([]) should return an empty array."""
+        a = np.array([], dtype=int)
+        r = rankdata(a)
+        assert_array_equal(r, np.array([], dtype=np.float64))
+        r = rankdata([])
+        assert_array_equal(r, np.array([], dtype=np.float64))
+
+    @pytest.mark.parametrize("shape", [(0, 1, 2)])
+    @pytest.mark.parametrize("axis", [None, *range(3)])
+    def test_empty_multidim(self, shape, axis):
+        a = np.empty(shape, dtype=int)
+        r = rankdata(a, axis=axis)
+        expected_shape = (0,) if axis is None else shape
+        assert_equal(r.shape, expected_shape)
+        assert_equal(r.dtype, np.float64)
+
+    def test_one(self):
+        """Check stats.rankdata with an array of length 1."""
+        data = [100]
+        a = np.array(data, dtype=int)
+        r = rankdata(a)
+        assert_array_equal(r, np.array([1.0], dtype=np.float64))
+        r = rankdata(data)
+        assert_array_equal(r, np.array([1.0], dtype=np.float64))
+
+    def test_basic(self):
+        """Basic tests of stats.rankdata."""
+        data = [100, 10, 50]
+        expected = np.array([3.0, 1.0, 2.0], dtype=np.float64)
+        a = np.array(data, dtype=int)
+        r = rankdata(a)
+        assert_array_equal(r, expected)
+        r = rankdata(data)
+        assert_array_equal(r, expected)
+
+        data = [40, 10, 30, 10, 50]
+        expected = np.array([4.0, 1.5, 3.0, 1.5, 5.0], dtype=np.float64)
+        a = np.array(data, dtype=int)
+        r = rankdata(a)
+        assert_array_equal(r, expected)
+        r = rankdata(data)
+        assert_array_equal(r, expected)
+
+        data = [20, 20, 20, 10, 10, 10]
+        expected = np.array([5.0, 5.0, 5.0, 2.0, 2.0, 2.0], dtype=np.float64)
+        a = np.array(data, dtype=int)
+        r = rankdata(a)
+        assert_array_equal(r, expected)
+        r = rankdata(data)
+        assert_array_equal(r, expected)
+        # The docstring states explicitly that the argument is flattened.
+        a2d = a.reshape(2, 3)
+        r = rankdata(a2d)
+        assert_array_equal(r, expected)
+
+    @skip_xp_invalid_arg
+    def test_rankdata_object_string(self):
+
+        def min_rank(a):
+            return [1 + sum(i < j for i in a) for j in a]
+
+        def max_rank(a):
+            return [sum(i <= j for i in a) for j in a]
+
+        def ordinal_rank(a):
+            return min_rank([(x, i) for i, x in enumerate(a)])
+
+        def average_rank(a):
+            return [(i + j) / 2.0 for i, j in zip(min_rank(a), max_rank(a))]
+
+        def dense_rank(a):
+            b = np.unique(a)
+            return [1 + sum(i < j for i in b) for j in a]
+
+        rankf = dict(min=min_rank, max=max_rank, ordinal=ordinal_rank,
+                     average=average_rank, dense=dense_rank)
+
+        def check_ranks(a):
+            for method in 'min', 'max', 'dense', 'ordinal', 'average':
+                out = rankdata(a, method=method)
+                assert_array_equal(out, rankf[method](a))
+
+        val = ['foo', 'bar', 'qux', 'xyz', 'abc', 'efg', 'ace', 'qwe', 'qaz']
+        check_ranks(np.random.choice(val, 200))
+        check_ranks(np.random.choice(val, 200).astype('object'))
+
+        val = np.array([0, 1, 2, 2.718, 3, 3.141], dtype='object')
+        check_ranks(np.random.choice(val, 200).astype('object'))
+
+    def test_large_int(self):
+        data = np.array([2**60, 2**60+1], dtype=np.uint64)
+        r = rankdata(data)
+        assert_array_equal(r, [1.0, 2.0])
+
+        data = np.array([2**60, 2**60+1], dtype=np.int64)
+        r = rankdata(data)
+        assert_array_equal(r, [1.0, 2.0])
+
+        data = np.array([2**60, -2**60+1], dtype=np.int64)
+        r = rankdata(data)
+        assert_array_equal(r, [2.0, 1.0])
+
+    def test_big_tie(self):
+        for n in [10000, 100000, 1000000]:
+            data = np.ones(n, dtype=int)
+            r = rankdata(data)
+            expected_rank = 0.5 * (n + 1)
+            assert_array_equal(r, expected_rank * data,
+                               "test failed with n=%d" % n)
+
+    def test_axis(self):
+        data = [[0, 2, 1],
+                [4, 2, 2]]
+        expected0 = [[1., 1.5, 1.],
+                     [2., 1.5, 2.]]
+        r0 = rankdata(data, axis=0)
+        assert_array_equal(r0, expected0)
+        expected1 = [[1., 3., 2.],
+                     [3., 1.5, 1.5]]
+        r1 = rankdata(data, axis=1)
+        assert_array_equal(r1, expected1)
+
+    methods = ["average", "min", "max", "dense", "ordinal"]
+    dtypes = [np.float64] + [np_long]*4
+
+    @pytest.mark.parametrize("axis", [0, 1])
+    @pytest.mark.parametrize("method, dtype", zip(methods, dtypes))
+    def test_size_0_axis(self, axis, method, dtype):
+        shape = (3, 0)
+        data = np.zeros(shape)
+        r = rankdata(data, method=method, axis=axis)
+        assert_equal(r.shape, shape)
+        assert_equal(r.dtype, dtype)
+
+    @pytest.mark.parametrize('axis', range(3))
+    @pytest.mark.parametrize('method', methods)
+    def test_nan_policy_omit_3d(self, axis, method):
+        shape = (20, 21, 22)
+        rng = np.random.RandomState(23983242)
+
+        a = rng.random(size=shape)
+        i = rng.random(size=shape) < 0.4
+        j = rng.random(size=shape) < 0.1
+        k = rng.random(size=shape) < 0.1
+        a[i] = np.nan
+        a[j] = -np.inf
+        a[k] - np.inf
+
+        def rank_1d_omit(a, method):
+            out = np.zeros_like(a)
+            i = np.isnan(a)
+            a_compressed = a[~i]
+            res = rankdata(a_compressed, method)
+            out[~i] = res
+            out[i] = np.nan
+            return out
+
+        def rank_omit(a, method, axis):
+            return np.apply_along_axis(lambda a: rank_1d_omit(a, method),
+                                       axis, a)
+
+        res = rankdata(a, method, axis=axis, nan_policy='omit')
+        res0 = rank_omit(a, method, axis=axis)
+
+        assert_array_equal(res, res0)
+
+    def test_nan_policy_2d_axis_none(self):
+        # 2 2d-array test with axis=None
+        data = [[0, np.nan, 3],
+                [4, 2, np.nan],
+                [1, 2, 2]]
+        assert_array_equal(rankdata(data, axis=None, nan_policy='omit'),
+                           [1., np.nan, 6., 7., 4., np.nan, 2., 4., 4.])
+        assert_array_equal(rankdata(data, axis=None, nan_policy='propagate'),
+                           [np.nan, np.nan, np.nan, np.nan, np.nan, np.nan,
+                            np.nan, np.nan, np.nan])
+
+    def test_nan_policy_raise(self):
+        # 1 1d-array test
+        data = [0, 2, 3, -2, np.nan, np.nan]
+        with pytest.raises(ValueError, match="The input contains nan"):
+            rankdata(data, nan_policy='raise')
+
+        # 2 2d-array test
+        data = [[0, np.nan, 3],
+                [4, 2, np.nan],
+                [np.nan, 2, 2]]
+
+        with pytest.raises(ValueError, match="The input contains nan"):
+            rankdata(data, axis=0, nan_policy="raise")
+
+        with pytest.raises(ValueError, match="The input contains nan"):
+            rankdata(data, axis=1, nan_policy="raise")
+
+    def test_nan_policy_propagate(self):
+        # 1 1d-array test
+        data = [0, 2, 3, -2, np.nan, np.nan]
+        assert_array_equal(rankdata(data, nan_policy='propagate'),
+                           [np.nan, np.nan, np.nan, np.nan, np.nan, np.nan])
+
+        # 2 2d-array test
+        data = [[0, np.nan, 3],
+                [4, 2, np.nan],
+                [1, 2, 2]]
+        assert_array_equal(rankdata(data, axis=0, nan_policy='propagate'),
+                           [[1, np.nan, np.nan],
+                            [3, np.nan, np.nan],
+                            [2, np.nan, np.nan]])
+        assert_array_equal(rankdata(data, axis=1, nan_policy='propagate'),
+                           [[np.nan, np.nan, np.nan],
+                            [np.nan, np.nan, np.nan],
+                            [1, 2.5, 2.5]])
+
+
+_cases = (
+    # values, method, expected
+    ([], 'average', []),
+    ([], 'min', []),
+    ([], 'max', []),
+    ([], 'dense', []),
+    ([], 'ordinal', []),
+    #
+    ([100], 'average', [1.0]),
+    ([100], 'min', [1.0]),
+    ([100], 'max', [1.0]),
+    ([100], 'dense', [1.0]),
+    ([100], 'ordinal', [1.0]),
+    #
+    ([100, 100, 100], 'average', [2.0, 2.0, 2.0]),
+    ([100, 100, 100], 'min', [1.0, 1.0, 1.0]),
+    ([100, 100, 100], 'max', [3.0, 3.0, 3.0]),
+    ([100, 100, 100], 'dense', [1.0, 1.0, 1.0]),
+    ([100, 100, 100], 'ordinal', [1.0, 2.0, 3.0]),
+    #
+    ([100, 300, 200], 'average', [1.0, 3.0, 2.0]),
+    ([100, 300, 200], 'min', [1.0, 3.0, 2.0]),
+    ([100, 300, 200], 'max', [1.0, 3.0, 2.0]),
+    ([100, 300, 200], 'dense', [1.0, 3.0, 2.0]),
+    ([100, 300, 200], 'ordinal', [1.0, 3.0, 2.0]),
+    #
+    ([100, 200, 300, 200], 'average', [1.0, 2.5, 4.0, 2.5]),
+    ([100, 200, 300, 200], 'min', [1.0, 2.0, 4.0, 2.0]),
+    ([100, 200, 300, 200], 'max', [1.0, 3.0, 4.0, 3.0]),
+    ([100, 200, 300, 200], 'dense', [1.0, 2.0, 3.0, 2.0]),
+    ([100, 200, 300, 200], 'ordinal', [1.0, 2.0, 4.0, 3.0]),
+    #
+    ([100, 200, 300, 200, 100], 'average', [1.5, 3.5, 5.0, 3.5, 1.5]),
+    ([100, 200, 300, 200, 100], 'min', [1.0, 3.0, 5.0, 3.0, 1.0]),
+    ([100, 200, 300, 200, 100], 'max', [2.0, 4.0, 5.0, 4.0, 2.0]),
+    ([100, 200, 300, 200, 100], 'dense', [1.0, 2.0, 3.0, 2.0, 1.0]),
+    ([100, 200, 300, 200, 100], 'ordinal', [1.0, 3.0, 5.0, 4.0, 2.0]),
+    #
+    ([10] * 30, 'ordinal', np.arange(1.0, 31.0)),
+)
+
+
+def test_cases():
+    for values, method, expected in _cases:
+        r = rankdata(values, method=method)
+        assert_array_equal(r, expected)

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_relative_risk.py

@@ -0,0 +1,95 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+from scipy.stats.contingency import relative_risk
+
+
+# Test just the calculation of the relative risk, including edge
+# cases that result in a relative risk of 0, inf or nan.
+@pytest.mark.parametrize(
+    'exposed_cases, exposed_total, control_cases, control_total, expected_rr',
+    [(1, 4, 3, 8, 0.25 / 0.375),
+     (0, 10, 5, 20, 0),
+     (0, 10, 0, 20, np.nan),
+     (5, 15, 0, 20, np.inf)]
+)
+def test_relative_risk(exposed_cases, exposed_total,
+                       control_cases, control_total, expected_rr):
+    result = relative_risk(exposed_cases, exposed_total,
+                           control_cases, control_total)
+    assert_allclose(result.relative_risk, expected_rr, rtol=1e-13)
+
+
+def test_relative_risk_confidence_interval():
+    result = relative_risk(exposed_cases=16, exposed_total=128,
+                           control_cases=24, control_total=256)
+    rr = result.relative_risk
+    ci = result.confidence_interval(confidence_level=0.95)
+    # The corresponding calculation in R using the epitools package.
+    #
+    # > library(epitools)
+    # > c <- matrix(c(232, 112, 24, 16), nrow=2)
+    # > result <- riskratio(c)
+    # > result$measure
+    #               risk ratio with 95% C.I.
+    # Predictor  estimate     lower    upper
+    #   Exposed1 1.000000        NA       NA
+    #   Exposed2 1.333333 0.7347317 2.419628
+    #
+    # The last line is the result that we want.
+    assert_allclose(rr, 4/3)
+    assert_allclose((ci.low, ci.high), (0.7347317, 2.419628), rtol=5e-7)
+
+
+def test_relative_risk_ci_conflevel0():
+    result = relative_risk(exposed_cases=4, exposed_total=12,
+                           control_cases=5, control_total=30)
+    rr = result.relative_risk
+    assert_allclose(rr, 2.0, rtol=1e-14)
+    ci = result.confidence_interval(0)
+    assert_allclose((ci.low, ci.high), (2.0, 2.0), rtol=1e-12)
+
+
+def test_relative_risk_ci_conflevel1():
+    result = relative_risk(exposed_cases=4, exposed_total=12,
+                           control_cases=5, control_total=30)
+    ci = result.confidence_interval(1)
+    assert_equal((ci.low, ci.high), (0, np.inf))
+
+
+def test_relative_risk_ci_edge_cases_00():
+    result = relative_risk(exposed_cases=0, exposed_total=12,
+                           control_cases=0, control_total=30)
+    assert_equal(result.relative_risk, np.nan)
+    ci = result.confidence_interval()
+    assert_equal((ci.low, ci.high), (np.nan, np.nan))
+
+
+def test_relative_risk_ci_edge_cases_01():
+    result = relative_risk(exposed_cases=0, exposed_total=12,
+                           control_cases=1, control_total=30)
+    assert_equal(result.relative_risk, 0)
+    ci = result.confidence_interval()
+    assert_equal((ci.low, ci.high), (0.0, np.nan))
+
+
+def test_relative_risk_ci_edge_cases_10():
+    result = relative_risk(exposed_cases=1, exposed_total=12,
+                           control_cases=0, control_total=30)
+    assert_equal(result.relative_risk, np.inf)
+    ci = result.confidence_interval()
+    assert_equal((ci.low, ci.high), (np.nan, np.inf))
+
+
+@pytest.mark.parametrize('ec, et, cc, ct', [(0, 0, 10, 20),
+                                            (-1, 10, 1, 5),
+                                            (1, 10, 0, 0),
+                                            (1, 10, -1, 4)])
+def test_relative_risk_bad_value(ec, et, cc, ct):
+    with pytest.raises(ValueError, match="must be an integer not less than"):
+        relative_risk(ec, et, cc, ct)
+
+
+def test_relative_risk_bad_type():
+    with pytest.raises(TypeError, match="must be an integer"):
+        relative_risk(1, 10, 2.0, 40)

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_sampling.py

@@ -0,0 +1,1447 @@
+import threading
+import pickle
+import pytest
+from copy import deepcopy
+import platform
+import sys
+import math
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal, suppress_warnings
+from scipy.stats.sampling import (
+    TransformedDensityRejection,
+    DiscreteAliasUrn,
+    DiscreteGuideTable,
+    NumericalInversePolynomial,
+    NumericalInverseHermite,
+    RatioUniforms,
+    SimpleRatioUniforms,
+    UNURANError
+)
+from pytest import raises as assert_raises
+from scipy import stats
+from scipy import special
+from scipy.stats import chisquare, cramervonmises
+from scipy.stats._distr_params import distdiscrete, distcont
+from scipy._lib._util import check_random_state
+
+
+# common test data: this data can be shared between all the tests.
+
+
+# Normal distribution shared between all the continuous methods
+class StandardNormal:
+    def pdf(self, x):
+        # normalization constant needed for NumericalInverseHermite
+        return 1./np.sqrt(2.*np.pi) * np.exp(-0.5 * x*x)
+
+    def dpdf(self, x):
+        return 1./np.sqrt(2.*np.pi) * -x * np.exp(-0.5 * x*x)
+
+    def cdf(self, x):
+        return special.ndtr(x)
+
+
+all_methods = [
+    ("TransformedDensityRejection", {"dist": StandardNormal()}),
+    ("DiscreteAliasUrn", {"dist": [0.02, 0.18, 0.8]}),
+    ("DiscreteGuideTable", {"dist": [0.02, 0.18, 0.8]}),
+    ("NumericalInversePolynomial", {"dist": StandardNormal()}),
+    ("NumericalInverseHermite", {"dist": StandardNormal()}),
+    ("SimpleRatioUniforms", {"dist": StandardNormal(), "mode": 0})
+]
+
+if (sys.implementation.name == 'pypy'
+        and sys.implementation.version < (7, 3, 10)):
+    # changed in PyPy for v7.3.10
+    floaterr = r"unsupported operand type for float\(\): 'list'"
+else:
+    floaterr = r"must be real number, not list"
+# Make sure an internal error occurs in UNU.RAN when invalid callbacks are
+# passed. Moreover, different generators throw different error messages.
+# So, in case of an `UNURANError`, we do not validate the error message.
+bad_pdfs_common = [
+    # Negative PDF
+    (lambda x: -x, UNURANError, r"..."),
+    # Returning wrong type
+    (lambda x: [], TypeError, floaterr),
+    # Undefined name inside the function
+    (lambda x: foo, NameError, r"name 'foo' is not defined"),  # type: ignore[name-defined]  # noqa: F821, E501
+    # Infinite value returned => Overflow error.
+    (lambda x: np.inf, UNURANError, r"..."),
+    # NaN value => internal error in UNU.RAN
+    (lambda x: np.nan, UNURANError, r"..."),
+    # signature of PDF wrong
+    (lambda: 1.0, TypeError, r"takes 0 positional arguments but 1 was given")
+]
+
+
+# same approach for dpdf
+bad_dpdf_common = [
+    # Infinite value returned.
+    (lambda x: np.inf, UNURANError, r"..."),
+    # NaN value => internal error in UNU.RAN
+    (lambda x: np.nan, UNURANError, r"..."),
+    # Returning wrong type
+    (lambda x: [], TypeError, floaterr),
+    # Undefined name inside the function
+    (lambda x: foo, NameError, r"name 'foo' is not defined"),  # type: ignore[name-defined]  # noqa: F821, E501
+    # signature of dPDF wrong
+    (lambda: 1.0, TypeError, r"takes 0 positional arguments but 1 was given")
+]
+
+
+# same approach for logpdf
+bad_logpdfs_common = [
+    # Returning wrong type
+    (lambda x: [], TypeError, floaterr),
+    # Undefined name inside the function
+    (lambda x: foo, NameError, r"name 'foo' is not defined"),  # type: ignore[name-defined]  # noqa: F821, E501
+    # Infinite value returned => Overflow error.
+    (lambda x: np.inf, UNURANError, r"..."),
+    # NaN value => internal error in UNU.RAN
+    (lambda x: np.nan, UNURANError, r"..."),
+    # signature of logpdf wrong
+    (lambda: 1.0, TypeError, r"takes 0 positional arguments but 1 was given")
+]
+
+
+bad_pv_common = [
+    ([], r"must contain at least one element"),
+    ([[1.0, 0.0]], r"wrong number of dimensions \(expected 1, got 2\)"),
+    ([0.2, 0.4, np.nan, 0.8], r"must contain only finite / non-nan values"),
+    ([0.2, 0.4, np.inf, 0.8], r"must contain only finite / non-nan values"),
+    ([0.0, 0.0], r"must contain at least one non-zero value"),
+]
+
+
+# size of the domains is incorrect
+bad_sized_domains = [
+    # > 2 elements in the domain
+    ((1, 2, 3), ValueError, r"must be a length 2 tuple"),
+    # empty domain
+    ((), ValueError, r"must be a length 2 tuple")
+]
+
+# domain values are incorrect
+bad_domains = [
+    ((2, 1), UNURANError, r"left >= right"),
+    ((1, 1), UNURANError, r"left >= right"),
+]
+
+# infinite and nan values present in domain.
+inf_nan_domains = [
+    # left >= right
+    ((10, 10), UNURANError, r"left >= right"),
+    ((np.inf, np.inf), UNURANError, r"left >= right"),
+    ((-np.inf, -np.inf), UNURANError, r"left >= right"),
+    ((np.inf, -np.inf), UNURANError, r"left >= right"),
+    # Also include nans in some of the domains.
+    ((-np.inf, np.nan), ValueError, r"only non-nan values"),
+    ((np.nan, np.inf), ValueError, r"only non-nan values")
+]
+
+# `nan` values present in domain. Some distributions don't support
+# infinite tails, so don't mix the nan values with infinities.
+nan_domains = [
+    ((0, np.nan), ValueError, r"only non-nan values"),
+    ((np.nan, np.nan), ValueError, r"only non-nan values")
+]
+
+
+# all the methods should throw errors for nan, bad sized, and bad valued
+# domains.
+@pytest.mark.parametrize("domain, err, msg",
+                         bad_domains + bad_sized_domains +
+                         nan_domains)  # type: ignore[operator]
+@pytest.mark.parametrize("method, kwargs", all_methods)
+def test_bad_domain(domain, err, msg, method, kwargs):
+    Method = getattr(stats.sampling, method)
+    with pytest.raises(err, match=msg):
+        Method(**kwargs, domain=domain)
+
+
+@pytest.mark.parametrize("method, kwargs", all_methods)
+def test_random_state(method, kwargs):
+    Method = getattr(stats.sampling, method)
+
+    # simple seed that works for any version of NumPy
+    seed = 123
+    rng1 = Method(**kwargs, random_state=seed)
+    rng2 = Method(**kwargs, random_state=seed)
+    assert_equal(rng1.rvs(100), rng2.rvs(100))
+
+    # global seed
+    np.random.seed(123)
+    rng1 = Method(**kwargs)
+    rvs1 = rng1.rvs(100)
+    np.random.seed(None)
+    rng2 = Method(**kwargs, random_state=123)
+    rvs2 = rng2.rvs(100)
+    assert_equal(rvs1, rvs2)
+
+    # Generator seed for new NumPy
+    # when a RandomState is given, it should take the bitgen_t
+    # member of the class and create a Generator instance.
+    seed1 = np.random.RandomState(np.random.MT19937(123))
+    seed2 = np.random.Generator(np.random.MT19937(123))
+    rng1 = Method(**kwargs, random_state=seed1)
+    rng2 = Method(**kwargs, random_state=seed2)
+    assert_equal(rng1.rvs(100), rng2.rvs(100))
+
+
+def test_set_random_state():
+    rng1 = TransformedDensityRejection(StandardNormal(), random_state=123)
+    rng2 = TransformedDensityRejection(StandardNormal())
+    rng2.set_random_state(123)
+    assert_equal(rng1.rvs(100), rng2.rvs(100))
+    rng = TransformedDensityRejection(StandardNormal(), random_state=123)
+    rvs1 = rng.rvs(100)
+    rng.set_random_state(123)
+    rvs2 = rng.rvs(100)
+    assert_equal(rvs1, rvs2)
+
+
+def test_threading_behaviour():
+    # Test if the API is thread-safe.
+    # This verifies if the lock mechanism and the use of `PyErr_Occurred`
+    # is correct.
+    errors = {"err1": None, "err2": None}
+
+    class Distribution:
+        def __init__(self, pdf_msg):
+            self.pdf_msg = pdf_msg
+
+        def pdf(self, x):
+            if 49.9 < x < 50.0:
+                raise ValueError(self.pdf_msg)
+            return x
+
+        def dpdf(self, x):
+            return 1
+
+    def func1():
+        dist = Distribution('foo')
+        rng = TransformedDensityRejection(dist, domain=(10, 100),
+                                          random_state=12)
+        try:
+            rng.rvs(100000)
+        except ValueError as e:
+            errors['err1'] = e.args[0]
+
+    def func2():
+        dist = Distribution('bar')
+        rng = TransformedDensityRejection(dist, domain=(10, 100),
+                                          random_state=2)
+        try:
+            rng.rvs(100000)
+        except ValueError as e:
+            errors['err2'] = e.args[0]
+
+    t1 = threading.Thread(target=func1)
+    t2 = threading.Thread(target=func2)
+
+    t1.start()
+    t2.start()
+
+    t1.join()
+    t2.join()
+
+    assert errors['err1'] == 'foo'
+    assert errors['err2'] == 'bar'
+
+
+@pytest.mark.parametrize("method, kwargs", all_methods)
+def test_pickle(method, kwargs):
+    Method = getattr(stats.sampling, method)
+    rng1 = Method(**kwargs, random_state=123)
+    obj = pickle.dumps(rng1)
+    rng2 = pickle.loads(obj)
+    assert_equal(rng1.rvs(100), rng2.rvs(100))
+
+
+@pytest.mark.parametrize("size", [None, 0, (0, ), 1, (10, 3), (2, 3, 4, 5),
+                                  (0, 0), (0, 1)])
+def test_rvs_size(size):
+    # As the `rvs` method is present in the base class and shared between
+    # all the classes, we can just test with one of the methods.
+    rng = TransformedDensityRejection(StandardNormal())
+    if size is None:
+        assert np.isscalar(rng.rvs(size))
+    else:
+        if np.isscalar(size):
+            size = (size, )
+        assert rng.rvs(size).shape == size
+
+
+def test_with_scipy_distribution():
+    # test if the setup works with SciPy's rv_frozen distributions
+    dist = stats.norm()
+    urng = np.random.default_rng(0)
+    rng = NumericalInverseHermite(dist, random_state=urng)
+    u = np.linspace(0, 1, num=100)
+    check_cont_samples(rng, dist, dist.stats())
+    assert_allclose(dist.ppf(u), rng.ppf(u))
+    # test if it works with `loc` and `scale`
+    dist = stats.norm(loc=10., scale=5.)
+    rng = NumericalInverseHermite(dist, random_state=urng)
+    check_cont_samples(rng, dist, dist.stats())
+    assert_allclose(dist.ppf(u), rng.ppf(u))
+    # check for discrete distributions
+    dist = stats.binom(10, 0.2)
+    rng = DiscreteAliasUrn(dist, random_state=urng)
+    domain = dist.support()
+    pv = dist.pmf(np.arange(domain[0], domain[1]+1))
+    check_discr_samples(rng, pv, dist.stats())
+
+
+def check_cont_samples(rng, dist, mv_ex, rtol=1e-7, atol=1e-1):
+    rvs = rng.rvs(100000)
+    mv = rvs.mean(), rvs.var()
+    # test the moments only if the variance is finite
+    if np.isfinite(mv_ex[1]):
+        assert_allclose(mv, mv_ex, rtol=rtol, atol=atol)
+    # Cramer Von Mises test for goodness-of-fit
+    rvs = rng.rvs(500)
+    dist.cdf = np.vectorize(dist.cdf)
+    pval = cramervonmises(rvs, dist.cdf).pvalue
+    assert pval > 0.1
+
+
+def check_discr_samples(rng, pv, mv_ex, rtol=1e-3, atol=1e-1):
+    rvs = rng.rvs(100000)
+    # test if the first few moments match
+    mv = rvs.mean(), rvs.var()
+    assert_allclose(mv, mv_ex, rtol=rtol, atol=atol)
+    # normalize
+    pv = pv / pv.sum()
+    # chi-squared test for goodness-of-fit
+    obs_freqs = np.zeros_like(pv)
+    _, freqs = np.unique(rvs, return_counts=True)
+    freqs = freqs / freqs.sum()
+    obs_freqs[:freqs.size] = freqs
+    pval = chisquare(obs_freqs, pv).pvalue
+    assert pval > 0.1
+
+
+def test_warning_center_not_in_domain():
+    # UNURAN will warn if the center provided or the one computed w/o the
+    # domain is outside of the domain
+    msg = "102 : center moved into domain of distribution"
+    with pytest.warns(RuntimeWarning, match=msg):
+        NumericalInversePolynomial(StandardNormal(), center=0, domain=(3, 5))
+    with pytest.warns(RuntimeWarning, match=msg):
+        NumericalInversePolynomial(StandardNormal(), domain=(3, 5))
+
+
+@pytest.mark.parametrize('method', ["SimpleRatioUniforms",
+                                    "NumericalInversePolynomial",
+                                    "TransformedDensityRejection"])
+def test_error_mode_not_in_domain(method):
+    # UNURAN raises an error if the mode is not in the domain
+    # the behavior is different compared to the case that center is not in the
+    # domain. mode is supposed to be the exact value, center can be an
+    # approximate value
+    Method = getattr(stats.sampling, method)
+    msg = "17 : mode not in domain"
+    with pytest.raises(UNURANError, match=msg):
+        Method(StandardNormal(), mode=0, domain=(3, 5))
+
+
+@pytest.mark.parametrize('method', ["NumericalInverseHermite",
+                                    "NumericalInversePolynomial"])
+class TestQRVS:
+    def test_input_validation(self, method):
+        match = "`qmc_engine` must be an instance of..."
+        with pytest.raises(ValueError, match=match):
+            Method = getattr(stats.sampling, method)
+            gen = Method(StandardNormal())
+            gen.qrvs(qmc_engine=0)
+
+        # issues with QMCEngines and old NumPy
+        Method = getattr(stats.sampling, method)
+        gen = Method(StandardNormal())
+
+        match = "`d` must be consistent with dimension of `qmc_engine`."
+        with pytest.raises(ValueError, match=match):
+            gen.qrvs(d=3, qmc_engine=stats.qmc.Halton(2))
+
+    qrngs = [None, stats.qmc.Sobol(1, seed=0), stats.qmc.Halton(3, seed=0)]
+    # `size=None` should not add anything to the shape, `size=1` should
+    sizes = [(None, tuple()), (1, (1,)), (4, (4,)),
+             ((4,), (4,)), ((2, 4), (2, 4))]  # type: ignore
+    # Neither `d=None` nor `d=1` should add anything to the shape
+    ds = [(None, tuple()), (1, tuple()), (3, (3,))]
+
+    @pytest.mark.parametrize('qrng', qrngs)
+    @pytest.mark.parametrize('size_in, size_out', sizes)
+    @pytest.mark.parametrize('d_in, d_out', ds)
+    def test_QRVS_shape_consistency(self, qrng, size_in, size_out,
+                                    d_in, d_out, method):
+        w32 = sys.platform == "win32" and platform.architecture()[0] == "32bit"
+        if w32 and method == "NumericalInversePolynomial":
+            pytest.xfail("NumericalInversePolynomial.qrvs fails for Win "
+                         "32-bit")
+
+        dist = StandardNormal()
+        Method = getattr(stats.sampling, method)
+        gen = Method(dist)
+
+        # If d and qrng.d are inconsistent, an error is raised
+        if d_in is not None and qrng is not None and qrng.d != d_in:
+            match = "`d` must be consistent with dimension of `qmc_engine`."
+            with pytest.raises(ValueError, match=match):
+                gen.qrvs(size_in, d=d_in, qmc_engine=qrng)
+            return
+
+        # Sometimes d is really determined by qrng
+        if d_in is None and qrng is not None and qrng.d != 1:
+            d_out = (qrng.d,)
+
+        shape_expected = size_out + d_out
+
+        qrng2 = deepcopy(qrng)
+        qrvs = gen.qrvs(size=size_in, d=d_in, qmc_engine=qrng)
+        if size_in is not None:
+            assert qrvs.shape == shape_expected
+
+        if qrng2 is not None:
+            uniform = qrng2.random(np.prod(size_in) or 1)
+            qrvs2 = stats.norm.ppf(uniform).reshape(shape_expected)
+            assert_allclose(qrvs, qrvs2, atol=1e-12)
+
+    def test_QRVS_size_tuple(self, method):
+        # QMCEngine samples are always of shape (n, d). When `size` is a tuple,
+        # we set `n = prod(size)` in the call to qmc_engine.random, transform
+        # the sample, and reshape it to the final dimensions. When we reshape,
+        # we need to be careful, because the _columns_ of the sample returned
+        # by a QMCEngine are "independent"-ish, but the elements within the
+        # columns are not. We need to make sure that this doesn't get mixed up
+        # by reshaping: qrvs[..., i] should remain "independent"-ish of
+        # qrvs[..., i+1], but the elements within qrvs[..., i] should be
+        # transformed from the same low-discrepancy sequence.
+
+        dist = StandardNormal()
+        Method = getattr(stats.sampling, method)
+        gen = Method(dist)
+
+        size = (3, 4)
+        d = 5
+        qrng = stats.qmc.Halton(d, seed=0)
+        qrng2 = stats.qmc.Halton(d, seed=0)
+
+        uniform = qrng2.random(np.prod(size))
+
+        qrvs = gen.qrvs(size=size, d=d, qmc_engine=qrng)
+        qrvs2 = stats.norm.ppf(uniform)
+
+        for i in range(d):
+            sample = qrvs[..., i]
+            sample2 = qrvs2[:, i].reshape(size)
+            assert_allclose(sample, sample2, atol=1e-12)
+
+
+class TestTransformedDensityRejection:
+    # Simple Custom Distribution
+    class dist0:
+        def pdf(self, x):
+            return 3/4 * (1-x*x)
+
+        def dpdf(self, x):
+            return 3/4 * (-2*x)
+
+        def cdf(self, x):
+            return 3/4 * (x - x**3/3 + 2/3)
+
+        def support(self):
+            return -1, 1
+
+    # Standard Normal Distribution
+    class dist1:
+        def pdf(self, x):
+            return stats.norm._pdf(x / 0.1)
+
+        def dpdf(self, x):
+            return -x / 0.01 * stats.norm._pdf(x / 0.1)
+
+        def cdf(self, x):
+            return stats.norm._cdf(x / 0.1)
+
+    # pdf with piecewise linear function as transformed density
+    # with T = -1/sqrt with shift. Taken from UNU.RAN test suite
+    # (from file t_tdr_ps.c)
+    class dist2:
+        def __init__(self, shift):
+            self.shift = shift
+
+        def pdf(self, x):
+            x -= self.shift
+            y = 1. / (abs(x) + 1.)
+            return 0.5 * y * y
+
+        def dpdf(self, x):
+            x -= self.shift
+            y = 1. / (abs(x) + 1.)
+            y = y * y * y
+            return y if (x < 0.) else -y
+
+        def cdf(self, x):
+            x -= self.shift
+            if x <= 0.:
+                return 0.5 / (1. - x)
+            else:
+                return 1. - 0.5 / (1. + x)
+
+    dists = [dist0(), dist1(), dist2(0.), dist2(10000.)]
+
+    # exact mean and variance of the distributions in the list dists
+    mv0 = [0., 4./15.]
+    mv1 = [0., 0.01]
+    mv2 = [0., np.inf]
+    mv3 = [10000., np.inf]
+    mvs = [mv0, mv1, mv2, mv3]
+
+    @pytest.mark.parametrize("dist, mv_ex",
+                             zip(dists, mvs))
+    def test_basic(self, dist, mv_ex):
+        with suppress_warnings() as sup:
+            # filter the warnings thrown by UNU.RAN
+            sup.filter(RuntimeWarning)
+            rng = TransformedDensityRejection(dist, random_state=42)
+        check_cont_samples(rng, dist, mv_ex)
+
+    # PDF 0 everywhere => bad construction points
+    bad_pdfs = [(lambda x: 0, UNURANError, r"50 : bad construction points.")]
+    bad_pdfs += bad_pdfs_common  # type: ignore[arg-type]
+
+    @pytest.mark.parametrize("pdf, err, msg", bad_pdfs)
+    def test_bad_pdf(self, pdf, err, msg):
+        class dist:
+            pass
+        dist.pdf = pdf
+        dist.dpdf = lambda x: 1  # an arbitrary dPDF
+        with pytest.raises(err, match=msg):
+            TransformedDensityRejection(dist)
+
+    @pytest.mark.parametrize("dpdf, err, msg", bad_dpdf_common)
+    def test_bad_dpdf(self, dpdf, err, msg):
+        class dist:
+            pass
+        dist.pdf = lambda x: x
+        dist.dpdf = dpdf
+        with pytest.raises(err, match=msg):
+            TransformedDensityRejection(dist, domain=(1, 10))
+
+    # test domains with inf + nan in them. need to write a custom test for
+    # this because not all methods support infinite tails.
+    @pytest.mark.parametrize("domain, err, msg", inf_nan_domains)
+    def test_inf_nan_domains(self, domain, err, msg):
+        with pytest.raises(err, match=msg):
+            TransformedDensityRejection(StandardNormal(), domain=domain)
+
+    @pytest.mark.parametrize("construction_points", [-1, 0, 0.1])
+    def test_bad_construction_points_scalar(self, construction_points):
+        with pytest.raises(ValueError, match=r"`construction_points` must be "
+                                             r"a positive integer."):
+            TransformedDensityRejection(
+                StandardNormal(), construction_points=construction_points
+            )
+
+    def test_bad_construction_points_array(self):
+        # empty array
+        construction_points = []
+        with pytest.raises(ValueError, match=r"`construction_points` must "
+                                             r"either be a "
+                                             r"scalar or a non-empty array."):
+            TransformedDensityRejection(
+                StandardNormal(), construction_points=construction_points
+            )
+
+        # construction_points not monotonically increasing
+        construction_points = [1, 1, 1, 1, 1, 1]
+        with pytest.warns(RuntimeWarning, match=r"33 : starting points not "
+                                                r"strictly monotonically "
+                                                r"increasing"):
+            TransformedDensityRejection(
+                StandardNormal(), construction_points=construction_points
+            )
+
+        # construction_points containing nans
+        construction_points = [np.nan, np.nan, np.nan]
+        with pytest.raises(UNURANError, match=r"50 : bad construction "
+                                              r"points."):
+            TransformedDensityRejection(
+                StandardNormal(), construction_points=construction_points
+            )
+
+        # construction_points out of domain
+        construction_points = [-10, 10]
+        with pytest.warns(RuntimeWarning, match=r"50 : starting point out of "
+                                                r"domain"):
+            TransformedDensityRejection(
+                StandardNormal(), domain=(-3, 3),
+                construction_points=construction_points
+            )
+
+    @pytest.mark.parametrize("c", [-1., np.nan, np.inf, 0.1, 1.])
+    def test_bad_c(self, c):
+        msg = r"`c` must either be -0.5 or 0."
+        with pytest.raises(ValueError, match=msg):
+            TransformedDensityRejection(StandardNormal(), c=-1.)
+
+    u = [np.linspace(0, 1, num=1000), [], [[]], [np.nan],
+         [-np.inf, np.nan, np.inf], 0,
+         [[np.nan, 0.5, 0.1], [0.2, 0.4, np.inf], [-2, 3, 4]]]
+
+    @pytest.mark.parametrize("u", u)
+    def test_ppf_hat(self, u):
+        # Increase the `max_squeeze_hat_ratio` so the ppf_hat is more
+        # accurate.
+        rng = TransformedDensityRejection(StandardNormal(),
+                                          max_squeeze_hat_ratio=0.9999)
+        # Older versions of NumPy throw RuntimeWarnings for comparisons
+        # with nan.
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, "invalid value encountered in greater")
+            sup.filter(RuntimeWarning, "invalid value encountered in "
+                                       "greater_equal")
+            sup.filter(RuntimeWarning, "invalid value encountered in less")
+            sup.filter(RuntimeWarning, "invalid value encountered in "
+                                       "less_equal")
+            res = rng.ppf_hat(u)
+            expected = stats.norm.ppf(u)
+        assert_allclose(res, expected, rtol=1e-3, atol=1e-5)
+        assert res.shape == expected.shape
+
+    def test_bad_dist(self):
+        # Empty distribution
+        class dist:
+            ...
+
+        msg = r"`pdf` required but not found."
+        with pytest.raises(ValueError, match=msg):
+            TransformedDensityRejection(dist)
+
+        # dPDF not present in dist
+        class dist:
+            pdf = lambda x: 1-x*x  # noqa: E731
+
+        msg = r"`dpdf` required but not found."
+        with pytest.raises(ValueError, match=msg):
+            TransformedDensityRejection(dist)
+
+
+class TestDiscreteAliasUrn:
+    # DAU fails on these probably because of large domains and small
+    # computation errors in PMF. Mean/SD match but chi-squared test fails.
+    basic_fail_dists = {
+        'nchypergeom_fisher',  # numerical errors on tails
+        'nchypergeom_wallenius',  # numerical errors on tails
+        'randint'  # fails on 32-bit ubuntu
+    }
+
+    @pytest.mark.parametrize("distname, params", distdiscrete)
+    def test_basic(self, distname, params):
+        if distname in self.basic_fail_dists:
+            msg = ("DAU fails on these probably because of large domains "
+                   "and small computation errors in PMF.")
+            pytest.skip(msg)
+        if not isinstance(distname, str):
+            dist = distname
+        else:
+            dist = getattr(stats, distname)
+        dist = dist(*params)
+        domain = dist.support()
+        if not np.isfinite(domain[1] - domain[0]):
+            # DAU only works with finite domain. So, skip the distributions
+            # with infinite tails.
+            pytest.skip("DAU only works with a finite domain.")
+        k = np.arange(domain[0], domain[1]+1)
+        pv = dist.pmf(k)
+        mv_ex = dist.stats('mv')
+        rng = DiscreteAliasUrn(dist, random_state=42)
+        check_discr_samples(rng, pv, mv_ex)
+
+    # Can't use bad_pmf_common here as we evaluate PMF early on to avoid
+    # unhelpful errors from UNU.RAN.
+    bad_pmf = [
+        # inf returned
+        (lambda x: np.inf, ValueError,
+         r"must contain only finite / non-nan values"),
+        # nan returned
+        (lambda x: np.nan, ValueError,
+         r"must contain only finite / non-nan values"),
+        # all zeros
+        (lambda x: 0.0, ValueError,
+         r"must contain at least one non-zero value"),
+        # Undefined name inside the function
+        (lambda x: foo, NameError,  # type: ignore[name-defined]  # noqa: F821
+         r"name 'foo' is not defined"),
+        # Returning wrong type.
+        (lambda x: [], ValueError,
+         r"setting an array element with a sequence."),
+        # probabilities < 0
+        (lambda x: -x, UNURANError,
+         r"50 : probability < 0"),
+        # signature of PMF wrong
+        (lambda: 1.0, TypeError,
+         r"takes 0 positional arguments but 1 was given")
+    ]
+
+    @pytest.mark.parametrize("pmf, err, msg", bad_pmf)
+    def test_bad_pmf(self, pmf, err, msg):
+        class dist:
+            pass
+        dist.pmf = pmf
+        with pytest.raises(err, match=msg):
+            DiscreteAliasUrn(dist, domain=(1, 10))
+
+    @pytest.mark.parametrize("pv", [[0.18, 0.02, 0.8],
+                                    [1.0, 2.0, 3.0, 4.0, 5.0, 6.0]])
+    def test_sampling_with_pv(self, pv):
+        pv = np.asarray(pv, dtype=np.float64)
+        rng = DiscreteAliasUrn(pv, random_state=123)
+        rng.rvs(100_000)
+        pv = pv / pv.sum()
+        variates = np.arange(0, len(pv))
+        # test if the first few moments match
+        m_expected = np.average(variates, weights=pv)
+        v_expected = np.average((variates - m_expected) ** 2, weights=pv)
+        mv_expected = m_expected, v_expected
+        check_discr_samples(rng, pv, mv_expected)
+
+    @pytest.mark.parametrize("pv, msg", bad_pv_common)
+    def test_bad_pv(self, pv, msg):
+        with pytest.raises(ValueError, match=msg):
+            DiscreteAliasUrn(pv)
+
+    # DAU doesn't support infinite tails. So, it should throw an error when
+    # inf is present in the domain.
+    inf_domain = [(-np.inf, np.inf), (np.inf, np.inf), (-np.inf, -np.inf),
+                  (0, np.inf), (-np.inf, 0)]
+
+    @pytest.mark.parametrize("domain", inf_domain)
+    def test_inf_domain(self, domain):
+        with pytest.raises(ValueError, match=r"must be finite"):
+            DiscreteAliasUrn(stats.binom(10, 0.2), domain=domain)
+
+    def test_bad_urn_factor(self):
+        with pytest.warns(RuntimeWarning, match=r"relative urn size < 1."):
+            DiscreteAliasUrn([0.5, 0.5], urn_factor=-1)
+
+    def test_bad_args(self):
+        msg = (r"`domain` must be provided when the "
+               r"probability vector is not available.")
+
+        class dist:
+            def pmf(self, x):
+                return x
+
+        with pytest.raises(ValueError, match=msg):
+            DiscreteAliasUrn(dist)
+
+    def test_gh19359(self):
+        pv = special.softmax(np.ones((1533,)))
+        rng = DiscreteAliasUrn(pv, random_state=42)
+        # check the correctness
+        check_discr_samples(rng, pv, (1532 / 2, (1532**2 - 1) / 12),
+                            rtol=5e-3)
+
+
+class TestNumericalInversePolynomial:
+    # Simple Custom Distribution
+    class dist0:
+        def pdf(self, x):
+            return 3/4 * (1-x*x)
+
+        def cdf(self, x):
+            return 3/4 * (x - x**3/3 + 2/3)
+
+        def support(self):
+            return -1, 1
+
+    # Standard Normal Distribution
+    class dist1:
+        def pdf(self, x):
+            return stats.norm._pdf(x / 0.1)
+
+        def cdf(self, x):
+            return stats.norm._cdf(x / 0.1)
+
+    # Sin 2 distribution
+    #          /  0.05 + 0.45*(1 +sin(2 Pi x))  if |x| <= 1
+    #  f(x) = <
+    #          \  0        otherwise
+    # Taken from UNU.RAN test suite (from file t_pinv.c)
+    class dist2:
+        def pdf(self, x):
+            return 0.05 + 0.45 * (1 + np.sin(2*np.pi*x))
+
+        def cdf(self, x):
+            return (0.05*(x + 1) +
+                    0.9*(1. + 2.*np.pi*(1 + x) - np.cos(2.*np.pi*x)) /
+                    (4.*np.pi))
+
+        def support(self):
+            return -1, 1
+
+    # Sin 10 distribution
+    #          /  0.05 + 0.45*(1 +sin(2 Pi x))  if |x| <= 5
+    #  f(x) = <
+    #          \  0        otherwise
+    # Taken from UNU.RAN test suite (from file t_pinv.c)
+    class dist3:
+        def pdf(self, x):
+            return 0.2 * (0.05 + 0.45 * (1 + np.sin(2*np.pi*x)))
+
+        def cdf(self, x):
+            return x/10. + 0.5 + 0.09/(2*np.pi) * (np.cos(10*np.pi) -
+                                                   np.cos(2*np.pi*x))
+
+        def support(self):
+            return -5, 5
+
+    dists = [dist0(), dist1(), dist2(), dist3()]
+
+    # exact mean and variance of the distributions in the list dists
+    mv0 = [0., 4./15.]
+    mv1 = [0., 0.01]
+    mv2 = [-0.45/np.pi, 2/3*0.5 - 0.45**2/np.pi**2]
+    mv3 = [-0.45/np.pi, 0.2 * 250/3 * 0.5 - 0.45**2/np.pi**2]
+    mvs = [mv0, mv1, mv2, mv3]
+
+    @pytest.mark.parametrize("dist, mv_ex",
+                             zip(dists, mvs))
+    def test_basic(self, dist, mv_ex):
+        rng = NumericalInversePolynomial(dist, random_state=42)
+        check_cont_samples(rng, dist, mv_ex)
+
+    @pytest.mark.xslow
+    @pytest.mark.parametrize("distname, params", distcont)
+    def test_basic_all_scipy_dists(self, distname, params):
+
+        very_slow_dists = ['anglit', 'gausshyper', 'kappa4',
+                           'ksone', 'kstwo', 'levy_l',
+                           'levy_stable', 'studentized_range',
+                           'trapezoid', 'triang', 'vonmises']
+        # for these distributions, some assertions fail due to minor
+        # numerical differences. They can be avoided either by changing
+        # the seed or by increasing the u_resolution.
+        fail_dists = ['chi2', 'fatiguelife', 'gibrat',
+                      'halfgennorm', 'lognorm', 'ncf',
+                      'ncx2', 'pareto', 't']
+        # for these distributions, skip the check for agreement between sample
+        # moments and true moments. We cannot expect them to pass due to the
+        # high variance of sample moments.
+        skip_sample_moment_check = ['rel_breitwigner']
+
+        if distname in very_slow_dists:
+            pytest.skip(f"PINV too slow for {distname}")
+        if distname in fail_dists:
+            pytest.skip(f"PINV fails for {distname}")
+        dist = (getattr(stats, distname)
+                if isinstance(distname, str)
+                else distname)
+        dist = dist(*params)
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning)
+            rng = NumericalInversePolynomial(dist, random_state=42)
+        if distname in skip_sample_moment_check:
+            return
+        check_cont_samples(rng, dist, [dist.mean(), dist.var()])
+
+    @pytest.mark.parametrize("pdf, err, msg", bad_pdfs_common)
+    def test_bad_pdf(self, pdf, err, msg):
+        class dist:
+            pass
+        dist.pdf = pdf
+        with pytest.raises(err, match=msg):
+            NumericalInversePolynomial(dist, domain=[0, 5])
+
+    @pytest.mark.parametrize("logpdf, err, msg", bad_logpdfs_common)
+    def test_bad_logpdf(self, logpdf, err, msg):
+        class dist:
+            pass
+        dist.logpdf = logpdf
+        with pytest.raises(err, match=msg):
+            NumericalInversePolynomial(dist, domain=[0, 5])
+
+    # test domains with inf + nan in them. need to write a custom test for
+    # this because not all methods support infinite tails.
+    @pytest.mark.parametrize("domain, err, msg", inf_nan_domains)
+    def test_inf_nan_domains(self, domain, err, msg):
+        with pytest.raises(err, match=msg):
+            NumericalInversePolynomial(StandardNormal(), domain=domain)
+
+    u = [
+        # test if quantile 0 and 1 return -inf and inf respectively and check
+        # the correctness of the PPF for equidistant points between 0 and 1.
+        np.linspace(0, 1, num=10000),
+        # test the PPF method for empty arrays
+        [], [[]],
+        # test if nans and infs return nan result.
+        [np.nan], [-np.inf, np.nan, np.inf],
+        # test if a scalar is returned for a scalar input.
+        0,
+        # test for arrays with nans, values greater than 1 and less than 0,
+        # and some valid values.
+        [[np.nan, 0.5, 0.1], [0.2, 0.4, np.inf], [-2, 3, 4]]
+    ]
+
+    @pytest.mark.parametrize("u", u)
+    def test_ppf(self, u):
+        dist = StandardNormal()
+        rng = NumericalInversePolynomial(dist, u_resolution=1e-14)
+        # Older versions of NumPy throw RuntimeWarnings for comparisons
+        # with nan.
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, "invalid value encountered in greater")
+            sup.filter(RuntimeWarning, "invalid value encountered in "
+                                       "greater_equal")
+            sup.filter(RuntimeWarning, "invalid value encountered in less")
+            sup.filter(RuntimeWarning, "invalid value encountered in "
+                                       "less_equal")
+            res = rng.ppf(u)
+            expected = stats.norm.ppf(u)
+        assert_allclose(res, expected, rtol=1e-11, atol=1e-11)
+        assert res.shape == expected.shape
+
+    x = [np.linspace(-10, 10, num=10000), [], [[]], [np.nan],
+         [-np.inf, np.nan, np.inf], 0,
+         [[np.nan, 0.5, 0.1], [0.2, 0.4, np.inf], [-np.inf, 3, 4]]]
+
+    @pytest.mark.parametrize("x", x)
+    def test_cdf(self, x):
+        dist = StandardNormal()
+        rng = NumericalInversePolynomial(dist, u_resolution=1e-14)
+        # Older versions of NumPy throw RuntimeWarnings for comparisons
+        # with nan.
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, "invalid value encountered in greater")
+            sup.filter(RuntimeWarning, "invalid value encountered in "
+                                       "greater_equal")
+            sup.filter(RuntimeWarning, "invalid value encountered in less")
+            sup.filter(RuntimeWarning, "invalid value encountered in "
+                                       "less_equal")
+            res = rng.cdf(x)
+            expected = stats.norm.cdf(x)
+        assert_allclose(res, expected, rtol=1e-11, atol=1e-11)
+        assert res.shape == expected.shape
+
+    @pytest.mark.slow
+    def test_u_error(self):
+        dist = StandardNormal()
+        rng = NumericalInversePolynomial(dist, u_resolution=1e-10)
+        max_error, mae = rng.u_error()
+        assert max_error < 1e-10
+        assert mae <= max_error
+        rng = NumericalInversePolynomial(dist, u_resolution=1e-14)
+        max_error, mae = rng.u_error()
+        assert max_error < 1e-14
+        assert mae <= max_error
+
+    bad_orders = [1, 4.5, 20, np.inf, np.nan]
+    bad_u_resolution = [1e-20, 1e-1, np.inf, np.nan]
+
+    @pytest.mark.parametrize("order", bad_orders)
+    def test_bad_orders(self, order):
+        dist = StandardNormal()
+
+        msg = r"`order` must be an integer in the range \[3, 17\]."
+        with pytest.raises(ValueError, match=msg):
+            NumericalInversePolynomial(dist, order=order)
+
+    @pytest.mark.parametrize("u_resolution", bad_u_resolution)
+    def test_bad_u_resolution(self, u_resolution):
+        msg = r"`u_resolution` must be between 1e-15 and 1e-5."
+        with pytest.raises(ValueError, match=msg):
+            NumericalInversePolynomial(StandardNormal(),
+                                       u_resolution=u_resolution)
+
+    def test_bad_args(self):
+
+        class BadDist:
+            def cdf(self, x):
+                return stats.norm._cdf(x)
+
+        dist = BadDist()
+        msg = r"Either of the methods `pdf` or `logpdf` must be specified"
+        with pytest.raises(ValueError, match=msg):
+            rng = NumericalInversePolynomial(dist)
+
+        dist = StandardNormal()
+        rng = NumericalInversePolynomial(dist)
+        msg = r"`sample_size` must be greater than or equal to 1000."
+        with pytest.raises(ValueError, match=msg):
+            rng.u_error(10)
+
+        class Distribution:
+            def pdf(self, x):
+                return np.exp(-0.5 * x*x)
+
+        dist = Distribution()
+        rng = NumericalInversePolynomial(dist)
+        msg = r"Exact CDF required but not found."
+        with pytest.raises(ValueError, match=msg):
+            rng.u_error()
+
+    def test_logpdf_pdf_consistency(self):
+        # 1. check that PINV works with pdf and logpdf only
+        # 2. check that generated ppf is the same (up to a small tolerance)
+
+        class MyDist:
+            pass
+
+        # create generator from dist with only pdf
+        dist_pdf = MyDist()
+        dist_pdf.pdf = lambda x: math.exp(-x*x/2)
+        rng1 = NumericalInversePolynomial(dist_pdf)
+
+        # create dist with only logpdf
+        dist_logpdf = MyDist()
+        dist_logpdf.logpdf = lambda x: -x*x/2
+        rng2 = NumericalInversePolynomial(dist_logpdf)
+
+        q = np.linspace(1e-5, 1-1e-5, num=100)
+        assert_allclose(rng1.ppf(q), rng2.ppf(q))
+
+
+class TestNumericalInverseHermite:
+    #         /  (1 +sin(2 Pi x))/2  if |x| <= 1
+    # f(x) = <
+    #         \  0        otherwise
+    # Taken from UNU.RAN test suite (from file t_hinv.c)
+    class dist0:
+        def pdf(self, x):
+            return 0.5*(1. + np.sin(2.*np.pi*x))
+
+        def dpdf(self, x):
+            return np.pi*np.cos(2.*np.pi*x)
+
+        def cdf(self, x):
+            return (1. + 2.*np.pi*(1 + x) - np.cos(2.*np.pi*x)) / (4.*np.pi)
+
+        def support(self):
+            return -1, 1
+
+    #         /  Max(sin(2 Pi x)),0)Pi/2  if -1 < x <0.5
+    # f(x) = <
+    #         \  0        otherwise
+    # Taken from UNU.RAN test suite (from file t_hinv.c)
+    class dist1:
+        def pdf(self, x):
+            if (x <= -0.5):
+                return np.sin((2. * np.pi) * x) * 0.5 * np.pi
+            if (x < 0.):
+                return 0.
+            if (x <= 0.5):
+                return np.sin((2. * np.pi) * x) * 0.5 * np.pi
+
+        def dpdf(self, x):
+            if (x <= -0.5):
+                return np.cos((2. * np.pi) * x) * np.pi * np.pi
+            if (x < 0.):
+                return 0.
+            if (x <= 0.5):
+                return np.cos((2. * np.pi) * x) * np.pi * np.pi
+
+        def cdf(self, x):
+            if (x <= -0.5):
+                return 0.25 * (1 - np.cos((2. * np.pi) * x))
+            if (x < 0.):
+                return 0.5
+            if (x <= 0.5):
+                return 0.75 - 0.25 * np.cos((2. * np.pi) * x)
+
+        def support(self):
+            return -1, 0.5
+
+    dists = [dist0(), dist1()]
+
+    # exact mean and variance of the distributions in the list dists
+    mv0 = [-1/(2*np.pi), 1/3 - 1/(4*np.pi*np.pi)]
+    mv1 = [-1/4, 3/8-1/(2*np.pi*np.pi) - 1/16]
+    mvs = [mv0, mv1]
+
+    @pytest.mark.parametrize("dist, mv_ex",
+                             zip(dists, mvs))
+    @pytest.mark.parametrize("order", [3, 5])
+    def test_basic(self, dist, mv_ex, order):
+        rng = NumericalInverseHermite(dist, order=order, random_state=42)
+        check_cont_samples(rng, dist, mv_ex)
+
+    # test domains with inf + nan in them. need to write a custom test for
+    # this because not all methods support infinite tails.
+    @pytest.mark.parametrize("domain, err, msg", inf_nan_domains)
+    def test_inf_nan_domains(self, domain, err, msg):
+        with pytest.raises(err, match=msg):
+            NumericalInverseHermite(StandardNormal(), domain=domain)
+
+    def basic_test_all_scipy_dists(self, distname, shapes):
+        slow_dists = {'ksone', 'kstwo', 'levy_stable', 'skewnorm'}
+        fail_dists = {'beta', 'gausshyper', 'geninvgauss', 'ncf', 'nct',
+                      'norminvgauss', 'genhyperbolic', 'studentized_range',
+                      'vonmises', 'kappa4', 'invgauss', 'wald'}
+
+        if distname in slow_dists:
+            pytest.skip("Distribution is too slow")
+        if distname in fail_dists:
+            # specific reasons documented in gh-13319
+            # https://github.com/scipy/scipy/pull/13319#discussion_r626188955
+            pytest.xfail("Fails - usually due to inaccurate CDF/PDF")
+
+        np.random.seed(0)
+
+        dist = getattr(stats, distname)(*shapes)
+        fni = NumericalInverseHermite(dist)
+
+        x = np.random.rand(10)
+        p_tol = np.max(np.abs(dist.ppf(x)-fni.ppf(x))/np.abs(dist.ppf(x)))
+        u_tol = np.max(np.abs(dist.cdf(fni.ppf(x)) - x))
+
+        assert p_tol < 1e-8
+        assert u_tol < 1e-12
+
+    @pytest.mark.filterwarnings('ignore::RuntimeWarning')
+    @pytest.mark.xslow
+    @pytest.mark.parametrize(("distname", "shapes"), distcont)
+    def test_basic_all_scipy_dists(self, distname, shapes):
+        # if distname == "truncnorm":
+        #     pytest.skip("Tested separately")
+        self.basic_test_all_scipy_dists(distname, shapes)
+
+    @pytest.mark.filterwarnings('ignore::RuntimeWarning')
+    def test_basic_truncnorm_gh17155(self):
+        self.basic_test_all_scipy_dists("truncnorm", (0.1, 2))
+
+    def test_input_validation(self):
+        match = r"`order` must be either 1, 3, or 5."
+        with pytest.raises(ValueError, match=match):
+            NumericalInverseHermite(StandardNormal(), order=2)
+
+        match = "`cdf` required but not found"
+        with pytest.raises(ValueError, match=match):
+            NumericalInverseHermite("norm")
+
+        match = "could not convert string to float"
+        with pytest.raises(ValueError, match=match):
+            NumericalInverseHermite(StandardNormal(),
+                                    u_resolution='ekki')
+
+    rngs = [None, 0, np.random.RandomState(0)]
+    rngs.append(np.random.default_rng(0))  # type: ignore
+    sizes = [(None, tuple()), (8, (8,)), ((4, 5, 6), (4, 5, 6))]
+
+    @pytest.mark.parametrize('rng', rngs)
+    @pytest.mark.parametrize('size_in, size_out', sizes)
+    def test_RVS(self, rng, size_in, size_out):
+        dist = StandardNormal()
+        fni = NumericalInverseHermite(dist)
+
+        rng2 = deepcopy(rng)
+        rvs = fni.rvs(size=size_in, random_state=rng)
+        if size_in is not None:
+            assert rvs.shape == size_out
+
+        if rng2 is not None:
+            rng2 = check_random_state(rng2)
+            uniform = rng2.uniform(size=size_in)
+            rvs2 = stats.norm.ppf(uniform)
+            assert_allclose(rvs, rvs2)
+
+    def test_inaccurate_CDF(self):
+        # CDF function with inaccurate tail cannot be inverted; see gh-13319
+        # https://github.com/scipy/scipy/pull/13319#discussion_r626188955
+        shapes = (2.3098496451481823, 0.6268795430096368)
+        match = ("98 : one or more intervals very short; possibly due to "
+                 "numerical problems with a pole or very flat tail")
+
+        # fails with default tol
+        with pytest.warns(RuntimeWarning, match=match):
+            NumericalInverseHermite(stats.beta(*shapes))
+
+        # no error with coarser tol
+        NumericalInverseHermite(stats.beta(*shapes), u_resolution=1e-8)
+
+    def test_custom_distribution(self):
+        dist1 = StandardNormal()
+        fni1 = NumericalInverseHermite(dist1)
+
+        dist2 = stats.norm()
+        fni2 = NumericalInverseHermite(dist2)
+
+        assert_allclose(fni1.rvs(random_state=0), fni2.rvs(random_state=0))
+
+    u = [
+        # check the correctness of the PPF for equidistant points between
+        # 0.02 and 0.98.
+        np.linspace(0., 1., num=10000),
+        # test the PPF method for empty arrays
+        [], [[]],
+        # test if nans and infs return nan result.
+        [np.nan], [-np.inf, np.nan, np.inf],
+        # test if a scalar is returned for a scalar input.
+        0,
+        # test for arrays with nans, values greater than 1 and less than 0,
+        # and some valid values.
+        [[np.nan, 0.5, 0.1], [0.2, 0.4, np.inf], [-2, 3, 4]]
+    ]
+
+    @pytest.mark.parametrize("u", u)
+    def test_ppf(self, u):
+        dist = StandardNormal()
+        rng = NumericalInverseHermite(dist, u_resolution=1e-12)
+        # Older versions of NumPy throw RuntimeWarnings for comparisons
+        # with nan.
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, "invalid value encountered in greater")
+            sup.filter(RuntimeWarning, "invalid value encountered in "
+                                       "greater_equal")
+            sup.filter(RuntimeWarning, "invalid value encountered in less")
+            sup.filter(RuntimeWarning, "invalid value encountered in "
+                                       "less_equal")
+            res = rng.ppf(u)
+            expected = stats.norm.ppf(u)
+        assert_allclose(res, expected, rtol=1e-9, atol=3e-10)
+        assert res.shape == expected.shape
+
+    @pytest.mark.slow
+    def test_u_error(self):
+        dist = StandardNormal()
+        rng = NumericalInverseHermite(dist, u_resolution=1e-10)
+        max_error, mae = rng.u_error()
+        assert max_error < 1e-10
+        assert mae <= max_error
+        with suppress_warnings() as sup:
+            # ignore warning about u-resolution being too small.
+            sup.filter(RuntimeWarning)
+            rng = NumericalInverseHermite(dist, u_resolution=1e-14)
+        max_error, mae = rng.u_error()
+        assert max_error < 1e-14
+        assert mae <= max_error
+
+
+class TestDiscreteGuideTable:
+    basic_fail_dists = {
+        'nchypergeom_fisher',  # numerical errors on tails
+        'nchypergeom_wallenius',  # numerical errors on tails
+        'randint'  # fails on 32-bit ubuntu
+    }
+
+    def test_guide_factor_gt3_raises_warning(self):
+        pv = [0.1, 0.3, 0.6]
+        urng = np.random.default_rng()
+        with pytest.warns(RuntimeWarning):
+            DiscreteGuideTable(pv, random_state=urng, guide_factor=7)
+
+    def test_guide_factor_zero_raises_warning(self):
+        pv = [0.1, 0.3, 0.6]
+        urng = np.random.default_rng()
+        with pytest.warns(RuntimeWarning):
+            DiscreteGuideTable(pv, random_state=urng, guide_factor=0)
+
+    def test_negative_guide_factor_raises_warning(self):
+        # This occurs from the UNU.RAN wrapper automatically.
+        # however it already gives a useful warning
+        # Here we just test that a warning is raised.
+        pv = [0.1, 0.3, 0.6]
+        urng = np.random.default_rng()
+        with pytest.warns(RuntimeWarning):
+            DiscreteGuideTable(pv, random_state=urng, guide_factor=-1)
+
+    @pytest.mark.parametrize("distname, params", distdiscrete)
+    def test_basic(self, distname, params):
+        if distname in self.basic_fail_dists:
+            msg = ("DGT fails on these probably because of large domains "
+                   "and small computation errors in PMF.")
+            pytest.skip(msg)
+
+        if not isinstance(distname, str):
+            dist = distname
+        else:
+            dist = getattr(stats, distname)
+
+        dist = dist(*params)
+        domain = dist.support()
+
+        if not np.isfinite(domain[1] - domain[0]):
+            # DGT only works with finite domain. So, skip the distributions
+            # with infinite tails.
+            pytest.skip("DGT only works with a finite domain.")
+
+        k = np.arange(domain[0], domain[1]+1)
+        pv = dist.pmf(k)
+        mv_ex = dist.stats('mv')
+        rng = DiscreteGuideTable(dist, random_state=42)
+        check_discr_samples(rng, pv, mv_ex)
+
+    u = [
+        # the correctness of the PPF for equidistant points between 0 and 1.
+        np.linspace(0, 1, num=10000),
+        # test the PPF method for empty arrays
+        [], [[]],
+        # test if nans and infs return nan result.
+        [np.nan], [-np.inf, np.nan, np.inf],
+        # test if a scalar is returned for a scalar input.
+        0,
+        # test for arrays with nans, values greater than 1 and less than 0,
+        # and some valid values.
+        [[np.nan, 0.5, 0.1], [0.2, 0.4, np.inf], [-2, 3, 4]]
+    ]
+
+    @pytest.mark.parametrize('u', u)
+    def test_ppf(self, u):
+        n, p = 4, 0.1
+        dist = stats.binom(n, p)
+        rng = DiscreteGuideTable(dist, random_state=42)
+
+        # Older versions of NumPy throw RuntimeWarnings for comparisons
+        # with nan.
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, "invalid value encountered in greater")
+            sup.filter(RuntimeWarning, "invalid value encountered in "
+                                       "greater_equal")
+            sup.filter(RuntimeWarning, "invalid value encountered in less")
+            sup.filter(RuntimeWarning, "invalid value encountered in "
+                                       "less_equal")
+
+            res = rng.ppf(u)
+            expected = stats.binom.ppf(u, n, p)
+        assert_equal(res.shape, expected.shape)
+        assert_equal(res, expected)
+
+    @pytest.mark.parametrize("pv, msg", bad_pv_common)
+    def test_bad_pv(self, pv, msg):
+        with pytest.raises(ValueError, match=msg):
+            DiscreteGuideTable(pv)
+
+    # DGT doesn't support infinite tails. So, it should throw an error when
+    # inf is present in the domain.
+    inf_domain = [(-np.inf, np.inf), (np.inf, np.inf), (-np.inf, -np.inf),
+                  (0, np.inf), (-np.inf, 0)]
+
+    @pytest.mark.parametrize("domain", inf_domain)
+    def test_inf_domain(self, domain):
+        with pytest.raises(ValueError, match=r"must be finite"):
+            DiscreteGuideTable(stats.binom(10, 0.2), domain=domain)
+
+
+class TestSimpleRatioUniforms:
+    # pdf with piecewise linear function as transformed density
+    # with T = -1/sqrt with shift. Taken from UNU.RAN test suite
+    # (from file t_srou.c)
+    class dist:
+        def __init__(self, shift):
+            self.shift = shift
+            self.mode = shift
+
+        def pdf(self, x):
+            x -= self.shift
+            y = 1. / (abs(x) + 1.)
+            return 0.5 * y * y
+
+        def cdf(self, x):
+            x -= self.shift
+            if x <= 0.:
+                return 0.5 / (1. - x)
+            else:
+                return 1. - 0.5 / (1. + x)
+
+    dists = [dist(0.), dist(10000.)]
+
+    # exact mean and variance of the distributions in the list dists
+    mv1 = [0., np.inf]
+    mv2 = [10000., np.inf]
+    mvs = [mv1, mv2]
+
+    @pytest.mark.parametrize("dist, mv_ex",
+                             zip(dists, mvs))
+    def test_basic(self, dist, mv_ex):
+        rng = SimpleRatioUniforms(dist, mode=dist.mode, random_state=42)
+        check_cont_samples(rng, dist, mv_ex)
+        rng = SimpleRatioUniforms(dist, mode=dist.mode,
+                                  cdf_at_mode=dist.cdf(dist.mode),
+                                  random_state=42)
+        check_cont_samples(rng, dist, mv_ex)
+
+    # test domains with inf + nan in them. need to write a custom test for
+    # this because not all methods support infinite tails.
+    @pytest.mark.parametrize("domain, err, msg", inf_nan_domains)
+    def test_inf_nan_domains(self, domain, err, msg):
+        with pytest.raises(err, match=msg):
+            SimpleRatioUniforms(StandardNormal(), domain=domain)
+
+    def test_bad_args(self):
+        # pdf_area < 0
+        with pytest.raises(ValueError, match=r"`pdf_area` must be > 0"):
+            SimpleRatioUniforms(StandardNormal(), mode=0, pdf_area=-1)
+
+
+class TestRatioUniforms:
+    """ Tests for rvs_ratio_uniforms.
+    """
+
+    def test_rv_generation(self):
+        # use KS test to check distribution of rvs
+        # normal distribution
+        f = stats.norm.pdf
+        v = np.sqrt(f(np.sqrt(2))) * np.sqrt(2)
+        u = np.sqrt(f(0))
+        gen = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=12345)
+        assert_equal(stats.kstest(gen.rvs(2500), 'norm')[1] > 0.25, True)
+
+        # exponential distribution
+        gen = RatioUniforms(lambda x: np.exp(-x), umax=1,
+                            vmin=0, vmax=2*np.exp(-1), random_state=12345)
+        assert_equal(stats.kstest(gen.rvs(1000), 'expon')[1] > 0.25, True)
+
+    def test_shape(self):
+        # test shape of return value depending on size parameter
+        f = stats.norm.pdf
+        v = np.sqrt(f(np.sqrt(2))) * np.sqrt(2)
+        u = np.sqrt(f(0))
+
+        gen1 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=1234)
+        gen2 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=1234)
+        gen3 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=1234)
+        r1, r2, r3 = gen1.rvs(3), gen2.rvs((3,)), gen3.rvs((3, 1))
+        assert_equal(r1, r2)
+        assert_equal(r2, r3.flatten())
+        assert_equal(r1.shape, (3,))
+        assert_equal(r3.shape, (3, 1))
+
+        gen4 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=12)
+        gen5 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=12)
+        r4, r5 = gen4.rvs(size=(3, 3, 3)), gen5.rvs(size=27)
+        assert_equal(r4.flatten(), r5)
+        assert_equal(r4.shape, (3, 3, 3))
+
+        gen6 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=1234)
+        gen7 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=1234)
+        gen8 = RatioUniforms(f, umax=u, vmin=-v, vmax=v, random_state=1234)
+        r6, r7, r8 = gen6.rvs(), gen7.rvs(1), gen8.rvs((1,))
+        assert_equal(r6, r7)
+        assert_equal(r7, r8)
+
+    def test_random_state(self):
+        f = stats.norm.pdf
+        v = np.sqrt(f(np.sqrt(2))) * np.sqrt(2)
+        umax = np.sqrt(f(0))
+        gen1 = RatioUniforms(f, umax=umax, vmin=-v, vmax=v, random_state=1234)
+        r1 = gen1.rvs(10)
+        np.random.seed(1234)
+        gen2 = RatioUniforms(f, umax=umax, vmin=-v, vmax=v)
+        r2 = gen2.rvs(10)
+        assert_equal(r1, r2)
+
+    def test_exceptions(self):
+        f = stats.norm.pdf
+        # need vmin < vmax
+        with assert_raises(ValueError, match="vmin must be smaller than vmax"):
+            RatioUniforms(pdf=f, umax=1, vmin=3, vmax=1)
+        with assert_raises(ValueError, match="vmin must be smaller than vmax"):
+            RatioUniforms(pdf=f, umax=1, vmin=1, vmax=1)
+        # need umax > 0
+        with assert_raises(ValueError, match="umax must be positive"):
+            RatioUniforms(pdf=f, umax=-1, vmin=1, vmax=3)
+        with assert_raises(ValueError, match="umax must be positive"):
+            RatioUniforms(pdf=f, umax=0, vmin=1, vmax=3)

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_sensitivity_analysis.py

@@ -0,0 +1,301 @@
+import numpy as np
+from numpy.testing import assert_allclose, assert_array_less
+import pytest
+
+from scipy import stats
+from scipy.stats import sobol_indices
+from scipy.stats._resampling import BootstrapResult
+from scipy.stats._sensitivity_analysis import (
+    BootstrapSobolResult, f_ishigami, sample_AB, sample_A_B
+)
+
+
+@pytest.fixture(scope='session')
+def ishigami_ref_indices():
+    """Reference values for Ishigami from Saltelli2007.
+
+    Chapter 4, exercise 5 pages 179-182.
+    """
+    a = 7.
+    b = 0.1
+
+    var = 0.5 + a**2/8 + b*np.pi**4/5 + b**2*np.pi**8/18
+    v1 = 0.5 + b*np.pi**4/5 + b**2*np.pi**8/50
+    v2 = a**2/8
+    v3 = 0
+    v12 = 0
+    # v13: mistake in the book, see other derivations e.g. in 10.1002/nme.4856
+    v13 = b**2*np.pi**8*8/225
+    v23 = 0
+
+    s_first = np.array([v1, v2, v3])/var
+    s_second = np.array([
+        [0., 0., v13],
+        [v12, 0., v23],
+        [v13, v23, 0.]
+    ])/var
+    s_total = s_first + s_second.sum(axis=1)
+
+    return s_first, s_total
+
+
+def f_ishigami_vec(x):
+    """Output of shape (2, n)."""
+    res = f_ishigami(x)
+    return res, res
+
+
+class TestSobolIndices:
+
+    dists = [
+        stats.uniform(loc=-np.pi, scale=2*np.pi)  # type: ignore[attr-defined]
+    ] * 3
+
+    def test_sample_AB(self):
+        # (d, n)
+        A = np.array(
+            [[1, 4, 7, 10],
+             [2, 5, 8, 11],
+             [3, 6, 9, 12]]
+        )
+        B = A + 100
+        # (d, d, n)
+        ref = np.array(
+            [[[101, 104, 107, 110],
+              [2, 5, 8, 11],
+              [3, 6, 9, 12]],
+             [[1, 4, 7, 10],
+              [102, 105, 108, 111],
+              [3, 6, 9, 12]],
+             [[1, 4, 7, 10],
+              [2, 5, 8, 11],
+              [103, 106, 109, 112]]]
+        )
+        AB = sample_AB(A=A, B=B)
+        assert_allclose(AB, ref)
+
+    @pytest.mark.xslow
+    @pytest.mark.xfail_on_32bit("Can't create large array for test")
+    @pytest.mark.parametrize(
+        'func',
+        [f_ishigami, pytest.param(f_ishigami_vec, marks=pytest.mark.slow)],
+        ids=['scalar', 'vector']
+    )
+    def test_ishigami(self, ishigami_ref_indices, func):
+        rng = np.random.default_rng(28631265345463262246170309650372465332)
+        res = sobol_indices(
+            func=func, n=4096,
+            dists=self.dists,
+            random_state=rng
+        )
+
+        if func.__name__ == 'f_ishigami_vec':
+            ishigami_ref_indices = [
+                    [ishigami_ref_indices[0], ishigami_ref_indices[0]],
+                    [ishigami_ref_indices[1], ishigami_ref_indices[1]]
+            ]
+
+        assert_allclose(res.first_order, ishigami_ref_indices[0], atol=1e-2)
+        assert_allclose(res.total_order, ishigami_ref_indices[1], atol=1e-2)
+
+        assert res._bootstrap_result is None
+        bootstrap_res = res.bootstrap(n_resamples=99)
+        assert isinstance(bootstrap_res, BootstrapSobolResult)
+        assert isinstance(res._bootstrap_result, BootstrapResult)
+
+        assert res._bootstrap_result.confidence_interval.low.shape[0] == 2
+        assert res._bootstrap_result.confidence_interval.low[1].shape \
+               == res.first_order.shape
+
+        assert bootstrap_res.first_order.confidence_interval.low.shape \
+               == res.first_order.shape
+        assert bootstrap_res.total_order.confidence_interval.low.shape \
+               == res.total_order.shape
+
+        assert_array_less(
+            bootstrap_res.first_order.confidence_interval.low, res.first_order
+        )
+        assert_array_less(
+            res.first_order, bootstrap_res.first_order.confidence_interval.high
+        )
+        assert_array_less(
+            bootstrap_res.total_order.confidence_interval.low, res.total_order
+        )
+        assert_array_less(
+            res.total_order, bootstrap_res.total_order.confidence_interval.high
+        )
+
+        # call again to use previous results and change a param
+        assert isinstance(
+            res.bootstrap(confidence_level=0.9, n_resamples=99),
+            BootstrapSobolResult
+        )
+        assert isinstance(res._bootstrap_result, BootstrapResult)
+
+    def test_func_dict(self, ishigami_ref_indices):
+        rng = np.random.default_rng(28631265345463262246170309650372465332)
+        n = 4096
+        dists = [
+            stats.uniform(loc=-np.pi, scale=2*np.pi),
+            stats.uniform(loc=-np.pi, scale=2*np.pi),
+            stats.uniform(loc=-np.pi, scale=2*np.pi)
+        ]
+
+        A, B = sample_A_B(n=n, dists=dists, random_state=rng)
+        AB = sample_AB(A=A, B=B)
+
+        func = {
+            'f_A': f_ishigami(A).reshape(1, -1),
+            'f_B': f_ishigami(B).reshape(1, -1),
+            'f_AB': f_ishigami(AB).reshape((3, 1, -1))
+        }
+
+        res = sobol_indices(
+            func=func, n=n,
+            dists=dists,
+            random_state=rng
+        )
+        assert_allclose(res.first_order, ishigami_ref_indices[0], atol=1e-2)
+
+        res = sobol_indices(
+            func=func, n=n,
+            random_state=rng
+        )
+        assert_allclose(res.first_order, ishigami_ref_indices[0], atol=1e-2)
+
+    def test_method(self, ishigami_ref_indices):
+        def jansen_sobol(f_A, f_B, f_AB):
+            """Jansen for S and Sobol' for St.
+
+            From Saltelli2010, table 2 formulations (c) and (e)."""
+            var = np.var([f_A, f_B], axis=(0, -1))
+
+            s = (var - 0.5*np.mean((f_B - f_AB)**2, axis=-1)) / var
+            st = np.mean(f_A*(f_A - f_AB), axis=-1) / var
+
+            return s.T, st.T
+
+        rng = np.random.default_rng(28631265345463262246170309650372465332)
+        res = sobol_indices(
+            func=f_ishigami, n=4096,
+            dists=self.dists,
+            method=jansen_sobol,
+            random_state=rng
+        )
+
+        assert_allclose(res.first_order, ishigami_ref_indices[0], atol=1e-2)
+        assert_allclose(res.total_order, ishigami_ref_indices[1], atol=1e-2)
+
+        def jansen_sobol_typed(
+            f_A: np.ndarray, f_B: np.ndarray, f_AB: np.ndarray
+        ) -> tuple[np.ndarray, np.ndarray]:
+            return jansen_sobol(f_A, f_B, f_AB)
+
+        _ = sobol_indices(
+            func=f_ishigami, n=8,
+            dists=self.dists,
+            method=jansen_sobol_typed,
+            random_state=rng
+        )
+
+    def test_normalization(self, ishigami_ref_indices):
+        rng = np.random.default_rng(28631265345463262246170309650372465332)
+        res = sobol_indices(
+            func=lambda x: f_ishigami(x) + 1000, n=4096,
+            dists=self.dists,
+            random_state=rng
+        )
+
+        assert_allclose(res.first_order, ishigami_ref_indices[0], atol=1e-2)
+        assert_allclose(res.total_order, ishigami_ref_indices[1], atol=1e-2)
+
+    def test_constant_function(self, ishigami_ref_indices):
+
+        def f_ishigami_vec_const(x):
+            """Output of shape (3, n)."""
+            res = f_ishigami(x)
+            return res, res * 0 + 10, res
+
+        rng = np.random.default_rng(28631265345463262246170309650372465332)
+        res = sobol_indices(
+            func=f_ishigami_vec_const, n=4096,
+            dists=self.dists,
+            random_state=rng
+        )
+
+        ishigami_vec_indices = [
+                [ishigami_ref_indices[0], [0, 0, 0], ishigami_ref_indices[0]],
+                [ishigami_ref_indices[1], [0, 0, 0], ishigami_ref_indices[1]]
+        ]
+
+        assert_allclose(res.first_order, ishigami_vec_indices[0], atol=1e-2)
+        assert_allclose(res.total_order, ishigami_vec_indices[1], atol=1e-2)
+
+    @pytest.mark.xfail_on_32bit("Can't create large array for test")
+    def test_more_converged(self, ishigami_ref_indices):
+        rng = np.random.default_rng(28631265345463262246170309650372465332)
+        res = sobol_indices(
+            func=f_ishigami, n=2**19,  # 524288
+            dists=self.dists,
+            random_state=rng
+        )
+
+        assert_allclose(res.first_order, ishigami_ref_indices[0], atol=1e-4)
+        assert_allclose(res.total_order, ishigami_ref_indices[1], atol=1e-4)
+
+    def test_raises(self):
+
+        message = r"Each distribution in `dists` must have method `ppf`"
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(n=0, func=f_ishigami, dists="uniform")
+
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(n=0, func=f_ishigami, dists=[lambda x: x])
+
+        message = r"The balance properties of Sobol'"
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(n=7, func=f_ishigami, dists=[stats.uniform()])
+
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(n=4.1, func=f_ishigami, dists=[stats.uniform()])
+
+        message = r"'toto' is not a valid 'method'"
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(n=0, func=f_ishigami, method='toto')
+
+        message = r"must have the following signature"
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(n=0, func=f_ishigami, method=lambda x: x)
+
+        message = r"'dists' must be defined when 'func' is a callable"
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(n=0, func=f_ishigami)
+
+        def func_wrong_shape_output(x):
+            return x.reshape(-1, 1)
+
+        message = r"'func' output should have a shape"
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(
+                n=2, func=func_wrong_shape_output, dists=[stats.uniform()]
+            )
+
+        message = r"When 'func' is a dictionary"
+        with pytest.raises(ValueError, match=message):
+            sobol_indices(
+                n=2, func={'f_A': [], 'f_AB': []}, dists=[stats.uniform()]
+            )
+
+        with pytest.raises(ValueError, match=message):
+            # f_B malformed
+            sobol_indices(
+                n=2,
+                func={'f_A': [1, 2], 'f_B': [3], 'f_AB': [5, 6, 7, 8]},
+            )
+
+        with pytest.raises(ValueError, match=message):
+            # f_AB malformed
+            sobol_indices(
+                n=2,
+                func={'f_A': [1, 2], 'f_B': [3, 4], 'f_AB': [5, 6, 7]},
+            )

parrot/lib/python3.10/site-packages/scipy/stats/tests/test_survival.py

@@ -0,0 +1,470 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+from scipy import stats
+from scipy.stats import _survival
+
+
+def _kaplan_meier_reference(times, censored):
+    # This is a very straightforward implementation of the Kaplan-Meier
+    # estimator that does almost everything differently from the implementation
+    # in stats.ecdf.
+
+    # Begin by sorting the raw data. Note that the order of death and loss
+    # at a given time matters: death happens first. See [2] page 461:
+    # "These conventions may be paraphrased by saying that deaths recorded as
+    # of an age t are treated as if they occurred slightly before t, and losses
+    # recorded as of an age t are treated as occurring slightly after t."
+    # We implement this by sorting the data first by time, then by `censored`,
+    # (which is 0 when there is a death and 1 when there is only a loss).
+    dtype = [('time', float), ('censored', int)]
+    data = np.array([(t, d) for t, d in zip(times, censored)], dtype=dtype)
+    data = np.sort(data, order=('time', 'censored'))
+    times = data['time']
+    died = np.logical_not(data['censored'])
+
+    m = times.size
+    n = np.arange(m, 0, -1)  # number at risk
+    sf = np.cumprod((n - died) / n)
+
+    # Find the indices of the *last* occurrence of unique times. The
+    # corresponding entries of `times` and `sf` are what we want.
+    _, indices = np.unique(times[::-1], return_index=True)
+    ref_times = times[-indices - 1]
+    ref_sf = sf[-indices - 1]
+    return ref_times, ref_sf
+
+
+class TestSurvival:
+
+    @staticmethod
+    def get_random_sample(rng, n_unique):
+        # generate random sample
+        unique_times = rng.random(n_unique)
+        # convert to `np.int32` to resolve `np.repeat` failure in 32-bit CI
+        repeats = rng.integers(1, 4, n_unique).astype(np.int32)
+        times = rng.permuted(np.repeat(unique_times, repeats))
+        censored = rng.random(size=times.size) > rng.random()
+        sample = stats.CensoredData.right_censored(times, censored)
+        return sample, times, censored
+
+    def test_input_validation(self):
+        message = '`sample` must be a one-dimensional sequence.'
+        with pytest.raises(ValueError, match=message):
+            stats.ecdf([[1]])
+        with pytest.raises(ValueError, match=message):
+            stats.ecdf(1)
+
+        message = '`sample` must not contain nan'
+        with pytest.raises(ValueError, match=message):
+            stats.ecdf([np.nan])
+
+        message = 'Currently, only uncensored and right-censored data...'
+        with pytest.raises(NotImplementedError, match=message):
+            stats.ecdf(stats.CensoredData.left_censored([1], censored=[True]))
+
+        message = 'method` must be one of...'
+        res = stats.ecdf([1, 2, 3])
+        with pytest.raises(ValueError, match=message):
+            res.cdf.confidence_interval(method='ekki-ekki')
+        with pytest.raises(ValueError, match=message):
+            res.sf.confidence_interval(method='shrubbery')
+
+        message = 'confidence_level` must be a scalar between 0 and 1'
+        with pytest.raises(ValueError, match=message):
+            res.cdf.confidence_interval(-1)
+        with pytest.raises(ValueError, match=message):
+            res.sf.confidence_interval([0.5, 0.6])
+
+        message = 'The confidence interval is undefined at some observations.'
+        with pytest.warns(RuntimeWarning, match=message):
+            ci = res.cdf.confidence_interval()
+
+        message = 'Confidence interval bounds do not implement...'
+        with pytest.raises(NotImplementedError, match=message):
+            ci.low.confidence_interval()
+        with pytest.raises(NotImplementedError, match=message):
+            ci.high.confidence_interval()
+
+    def test_edge_cases(self):
+        res = stats.ecdf([])
+        assert_equal(res.cdf.quantiles, [])
+        assert_equal(res.cdf.probabilities, [])
+
+        res = stats.ecdf([1])
+        assert_equal(res.cdf.quantiles, [1])
+        assert_equal(res.cdf.probabilities, [1])
+
+    def test_unique(self):
+        # Example with unique observations; `stats.ecdf` ref. [1] page 80
+        sample = [6.23, 5.58, 7.06, 6.42, 5.20]
+        res = stats.ecdf(sample)
+        ref_x = np.sort(np.unique(sample))
+        ref_cdf = np.arange(1, 6) / 5
+        ref_sf = 1 - ref_cdf
+        assert_equal(res.cdf.quantiles, ref_x)
+        assert_equal(res.cdf.probabilities, ref_cdf)
+        assert_equal(res.sf.quantiles, ref_x)
+        assert_equal(res.sf.probabilities, ref_sf)
+
+    def test_nonunique(self):
+        # Example with non-unique observations; `stats.ecdf` ref. [1] page 82
+        sample = [0, 2, 1, 2, 3, 4]
+        res = stats.ecdf(sample)
+        ref_x = np.sort(np.unique(sample))
+        ref_cdf = np.array([1/6, 2/6, 4/6, 5/6, 1])
+        ref_sf = 1 - ref_cdf
+        assert_equal(res.cdf.quantiles, ref_x)
+        assert_equal(res.cdf.probabilities, ref_cdf)
+        assert_equal(res.sf.quantiles, ref_x)
+        assert_equal(res.sf.probabilities, ref_sf)
+
+    def test_evaluate_methods(self):
+        # Test CDF and SF `evaluate` methods
+        rng = np.random.default_rng(1162729143302572461)
+        sample, _, _ = self.get_random_sample(rng, 15)
+        res = stats.ecdf(sample)
+        x = res.cdf.quantiles
+        xr = x + np.diff(x, append=x[-1]+1)/2  # right shifted points
+
+        assert_equal(res.cdf.evaluate(x), res.cdf.probabilities)
+        assert_equal(res.cdf.evaluate(xr), res.cdf.probabilities)
+        assert_equal(res.cdf.evaluate(x[0]-1), 0)  # CDF starts at 0
+        assert_equal(res.cdf.evaluate([-np.inf, np.inf]), [0, 1])
+
+        assert_equal(res.sf.evaluate(x), res.sf.probabilities)
+        assert_equal(res.sf.evaluate(xr), res.sf.probabilities)
+        assert_equal(res.sf.evaluate(x[0]-1), 1)  # SF starts at 1
+        assert_equal(res.sf.evaluate([-np.inf, np.inf]), [1, 0])
+
+    # ref. [1] page 91
+    t1 = [37, 43, 47, 56, 60, 62, 71, 77, 80, 81]  # times
+    d1 = [0, 0, 1, 1, 0, 0, 0, 1, 1, 1]  # 1 means deaths (not censored)
+    r1 = [1, 1, 0.875, 0.75, 0.75, 0.75, 0.75, 0.5, 0.25, 0]  # reference SF
+
+    # https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_survival/BS704_Survival5.html
+    t2 = [8, 12, 26, 14, 21, 27, 8, 32, 20, 40]
+    d2 = [1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
+    r2 = [0.9, 0.788, 0.675, 0.675, 0.54, 0.405, 0.27, 0.27, 0.27]
+    t3 = [33, 28, 41, 48, 48, 25, 37, 48, 25, 43]
+    d3 = [1, 1, 1, 0, 0, 0, 0, 0, 0, 0]
+    r3 = [1, 0.875, 0.75, 0.75, 0.6, 0.6, 0.6]
+
+    # https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_survival/bs704_survival4.html
+    t4 = [24, 3, 11, 19, 24, 13, 14, 2, 18, 17,
+          24, 21, 12, 1, 10, 23, 6, 5, 9, 17]
+    d4 = [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1]
+    r4 = [0.95, 0.95, 0.897, 0.844, 0.844, 0.844, 0.844, 0.844, 0.844,
+          0.844, 0.76, 0.676, 0.676, 0.676, 0.676, 0.507, 0.507]
+
+    # https://www.real-statistics.com/survival-analysis/kaplan-meier-procedure/confidence-interval-for-the-survival-function/
+    t5 = [3, 5, 8, 10, 5, 5, 8, 12, 15, 14, 2, 11, 10, 9, 12, 5, 8, 11]
+    d5 = [1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1]
+    r5 = [0.944, 0.889, 0.722, 0.542, 0.542, 0.542, 0.361, 0.181, 0.181, 0.181]
+
+    @pytest.mark.parametrize("case", [(t1, d1, r1), (t2, d2, r2), (t3, d3, r3),
+                                      (t4, d4, r4), (t5, d5, r5)])
+    def test_right_censored_against_examples(self, case):
+        # test `ecdf` against other implementations on example problems
+        times, died, ref = case
+        sample = stats.CensoredData.right_censored(times, np.logical_not(died))
+        res = stats.ecdf(sample)
+        assert_allclose(res.sf.probabilities, ref, atol=1e-3)
+        assert_equal(res.sf.quantiles, np.sort(np.unique(times)))
+
+        # test reference implementation against other implementations
+        res = _kaplan_meier_reference(times, np.logical_not(died))
+        assert_equal(res[0], np.sort(np.unique(times)))
+        assert_allclose(res[1], ref, atol=1e-3)
+
+    @pytest.mark.parametrize('seed', [182746786639392128, 737379171436494115,
+                                      576033618403180168, 308115465002673650])
+    def test_right_censored_against_reference_implementation(self, seed):
+        # test `ecdf` against reference implementation on random problems
+        rng = np.random.default_rng(seed)
+        n_unique = rng.integers(10, 100)
+        sample, times, censored = self.get_random_sample(rng, n_unique)
+        res = stats.ecdf(sample)
+        ref = _kaplan_meier_reference(times, censored)
+        assert_allclose(res.sf.quantiles, ref[0])
+        assert_allclose(res.sf.probabilities, ref[1])
+
+        # If all observations are uncensored, the KM estimate should match
+        # the usual estimate for uncensored data
+        sample = stats.CensoredData(uncensored=times)
+        res = _survival._ecdf_right_censored(sample)  # force Kaplan-Meier
+        ref = stats.ecdf(times)
+        assert_equal(res[0], ref.sf.quantiles)
+        assert_allclose(res[1], ref.cdf.probabilities, rtol=1e-14)
+        assert_allclose(res[2], ref.sf.probabilities, rtol=1e-14)
+
+    def test_right_censored_ci(self):
+        # test "greenwood" confidence interval against example 4 (URL above).
+        times, died = self.t4, self.d4
+        sample = stats.CensoredData.right_censored(times, np.logical_not(died))
+        res = stats.ecdf(sample)
+        ref_allowance = [0.096, 0.096, 0.135, 0.162, 0.162, 0.162, 0.162,
+                         0.162, 0.162, 0.162, 0.214, 0.246, 0.246, 0.246,
+                         0.246, 0.341, 0.341]
+
+        sf_ci = res.sf.confidence_interval()
+        cdf_ci = res.cdf.confidence_interval()
+        allowance = res.sf.probabilities - sf_ci.low.probabilities
+
+        assert_allclose(allowance, ref_allowance, atol=1e-3)
+        assert_allclose(sf_ci.low.probabilities,
+                        np.clip(res.sf.probabilities - allowance, 0, 1))
+        assert_allclose(sf_ci.high.probabilities,
+                        np.clip(res.sf.probabilities + allowance, 0, 1))
+        assert_allclose(cdf_ci.low.probabilities,
+                        np.clip(res.cdf.probabilities - allowance, 0, 1))
+        assert_allclose(cdf_ci.high.probabilities,
+                        np.clip(res.cdf.probabilities + allowance, 0, 1))
+
+        # test "log-log" confidence interval against Mathematica
+        # e = {24, 3, 11, 19, 24, 13, 14, 2, 18, 17, 24, 21, 12, 1, 10, 23, 6, 5,
+        #      9, 17}
+        # ci = {1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0}
+        # R = EventData[e, ci]
+        # S = SurvivalModelFit[R]
+        # S["PointwiseIntervals", ConfidenceLevel->0.95,
+        #   ConfidenceTransform->"LogLog"]
+
+        ref_low = [0.694743, 0.694743, 0.647529, 0.591142, 0.591142, 0.591142,
+                   0.591142, 0.591142, 0.591142, 0.591142, 0.464605, 0.370359,
+                   0.370359, 0.370359, 0.370359, 0.160489, 0.160489]
+        ref_high = [0.992802, 0.992802, 0.973299, 0.947073, 0.947073, 0.947073,
+                    0.947073, 0.947073, 0.947073, 0.947073, 0.906422, 0.856521,
+                    0.856521, 0.856521, 0.856521, 0.776724, 0.776724]
+        sf_ci = res.sf.confidence_interval(method='log-log')
+        assert_allclose(sf_ci.low.probabilities, ref_low, atol=1e-6)
+        assert_allclose(sf_ci.high.probabilities, ref_high, atol=1e-6)
+
+    def test_right_censored_ci_example_5(self):
+        # test "exponential greenwood" confidence interval against example 5
+        times, died = self.t5, self.d5
+        sample = stats.CensoredData.right_censored(times, np.logical_not(died))
+        res = stats.ecdf(sample)
+        lower = np.array([0.66639, 0.624174, 0.456179, 0.287822, 0.287822,
+                          0.287822, 0.128489, 0.030957, 0.030957, 0.030957])
+        upper = np.array([0.991983, 0.970995, 0.87378, 0.739467, 0.739467,
+                          0.739467, 0.603133, 0.430365, 0.430365, 0.430365])
+
+        sf_ci = res.sf.confidence_interval(method='log-log')
+        cdf_ci = res.cdf.confidence_interval(method='log-log')
+
+        assert_allclose(sf_ci.low.probabilities, lower, atol=1e-5)
+        assert_allclose(sf_ci.high.probabilities, upper, atol=1e-5)
+        assert_allclose(cdf_ci.low.probabilities, 1-upper, atol=1e-5)
+        assert_allclose(cdf_ci.high.probabilities, 1-lower, atol=1e-5)
+
+        # Test against R's `survival` library `survfit` function, 90%CI
+        # library(survival)
+        # options(digits=16)
+        # time = c(3, 5, 8, 10, 5, 5, 8, 12, 15, 14, 2, 11, 10, 9, 12, 5, 8, 11)
+        # status = c(1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1)
+        # res = survfit(Surv(time, status)
+        # ~1, conf.type = "log-log", conf.int = 0.90)
+        # res$time; res$lower; res$upper
+        low = [0.74366748406861172, 0.68582332289196246, 0.50596835651480121,
+               0.32913131413336727, 0.32913131413336727, 0.32913131413336727,
+               0.15986912028781664, 0.04499539918147757, 0.04499539918147757,
+               0.04499539918147757]
+        high = [0.9890291867238429, 0.9638835422144144, 0.8560366823086629,
+                0.7130167643978450, 0.7130167643978450, 0.7130167643978450,
+                0.5678602982997164, 0.3887616766886558, 0.3887616766886558,
+                0.3887616766886558]
+        sf_ci = res.sf.confidence_interval(method='log-log',
+                                           confidence_level=0.9)
+        assert_allclose(sf_ci.low.probabilities, low)
+        assert_allclose(sf_ci.high.probabilities, high)
+
+        # And with conf.type = "plain"
+        low = [0.8556383113628162, 0.7670478794850761, 0.5485720663578469,
+               0.3441515412527123, 0.3441515412527123, 0.3441515412527123,
+               0.1449184105424544, 0., 0., 0.]
+        high = [1., 1., 0.8958723780865975, 0.7391817920806210,
+                0.7391817920806210, 0.7391817920806210, 0.5773038116797676,
+                0.3642270254596720, 0.3642270254596720, 0.3642270254596720]
+        sf_ci = res.sf.confidence_interval(confidence_level=0.9)
+        assert_allclose(sf_ci.low.probabilities, low)
+        assert_allclose(sf_ci.high.probabilities, high)
+
+    def test_right_censored_ci_nans(self):
+        # test `ecdf` confidence interval on a problem that results in NaNs
+        times, died = self.t1, self.d1
+        sample = stats.CensoredData.right_censored(times, np.logical_not(died))
+        res = stats.ecdf(sample)
+
+        # Reference values generated with Matlab
+        # format long
+        # t = [37 43 47 56 60 62 71 77 80 81];
+        # d = [0 0 1 1 0 0 0 1 1 1];
+        # censored = ~d1;
+        # [f, x, flo, fup] = ecdf(t, 'Censoring', censored, 'Alpha', 0.05);
+        x = [37, 47, 56, 77, 80, 81]
+        flo = [np.nan, 0, 0, 0.052701464070711, 0.337611126231790, np.nan]
+        fup = [np.nan, 0.35417230377, 0.5500569798, 0.9472985359, 1.0, np.nan]
+        i = np.searchsorted(res.cdf.quantiles, x)
+
+        message = "The confidence interval is undefined at some observations"
+        with pytest.warns(RuntimeWarning, match=message):
+            ci = res.cdf.confidence_interval()
+
+        # Matlab gives NaN as the first element of the CIs. Mathematica agrees,
+        # but R's survfit does not. It makes some sense, but it's not what the
+        # formula gives, so skip that element.
+        assert_allclose(ci.low.probabilities[i][1:], flo[1:])
+        assert_allclose(ci.high.probabilities[i][1:], fup[1:])
+
+        # [f, x, flo, fup] = ecdf(t, 'Censoring', censored, 'Function',
+        #                        'survivor', 'Alpha', 0.05);
+        flo = [np.nan, 0.64582769623, 0.449943020228, 0.05270146407, 0, np.nan]
+        fup = [np.nan, 1.0, 1.0, 0.947298535929289, 0.662388873768210, np.nan]
+        i = np.searchsorted(res.cdf.quantiles, x)
+
+        with pytest.warns(RuntimeWarning, match=message):
+            ci = res.sf.confidence_interval()
+
+        assert_allclose(ci.low.probabilities[i][1:], flo[1:])
+        assert_allclose(ci.high.probabilities[i][1:], fup[1:])
+
+        # With the same data, R's `survival` library `survfit` function
+        # doesn't produce the leading NaN
+        # library(survival)
+        # options(digits=16)
+        # time = c(37, 43, 47, 56, 60, 62, 71, 77, 80, 81)
+        # status = c(0, 0, 1, 1, 0, 0, 0, 1, 1, 1)
+        # res = survfit(Surv(time, status)
+        # ~1, conf.type = "plain", conf.int = 0.95)
+        # res$time
+        # res$lower
+        # res$upper
+        low = [1., 1., 0.64582769623233816, 0.44994302022779326,
+               0.44994302022779326, 0.44994302022779326, 0.44994302022779326,
+               0.05270146407071086, 0., np.nan]
+        high = [1., 1., 1., 1., 1., 1., 1., 0.9472985359292891,
+                0.6623888737682101, np.nan]
+        assert_allclose(ci.low.probabilities, low)
+        assert_allclose(ci.high.probabilities, high)
+
+        # It does with conf.type="log-log", as do we
+        with pytest.warns(RuntimeWarning, match=message):
+            ci = res.sf.confidence_interval(method='log-log')
+        low = [np.nan, np.nan, 0.38700001403202522, 0.31480711370551911,
+               0.31480711370551911, 0.31480711370551911, 0.31480711370551911,
+               0.08048821148507734, 0.01049958986680601, np.nan]
+        high = [np.nan, np.nan, 0.9813929658789660, 0.9308983170906275,
+                0.9308983170906275, 0.9308983170906275, 0.9308983170906275,
+                0.8263946341076415, 0.6558775085110887, np.nan]
+        assert_allclose(ci.low.probabilities, low)
+        assert_allclose(ci.high.probabilities, high)
+
+    def test_right_censored_against_uncensored(self):
+        rng = np.random.default_rng(7463952748044886637)
+        sample = rng.integers(10, 100, size=1000)
+        censored = np.zeros_like(sample)
+        censored[np.argmax(sample)] = True
+        res = stats.ecdf(sample)
+        ref = stats.ecdf(stats.CensoredData.right_censored(sample, censored))
+        assert_equal(res.sf.quantiles, ref.sf.quantiles)
+        assert_equal(res.sf._n, ref.sf._n)
+        assert_equal(res.sf._d[:-1], ref.sf._d[:-1])  # difference @ [-1]
+        assert_allclose(res.sf._sf[:-1], ref.sf._sf[:-1], rtol=1e-14)
+
+    def test_plot_iv(self):
+        rng = np.random.default_rng(1769658657308472721)
+        n_unique = rng.integers(10, 100)
+        sample, _, _ = self.get_random_sample(rng, n_unique)
+        res = stats.ecdf(sample)
+
+        try:
+            import matplotlib.pyplot as plt  # noqa: F401
+            res.sf.plot()  # no other errors occur
+        except (ModuleNotFoundError, ImportError):
+            # Avoid trying to call MPL with numpy 2.0-dev, because that fails
+            # too often due to ABI mismatches and is hard to avoid. This test
+            # will work fine again once MPL has done a 2.0-compatible release.
+            if not np.__version__.startswith('2.0.0.dev0'):
+                message = r"matplotlib must be installed to use method `plot`."
+                with pytest.raises(ModuleNotFoundError, match=message):
+                    res.sf.plot()
+
+
+class TestLogRank:
+
+    @pytest.mark.parametrize(
+        "x, y, statistic, pvalue",
+        # Results validate with R
+        # library(survival)
+        # options(digits=16)
+        #
+        # futime_1 <- c(8, 12, 26, 14, 21, 27, 8, 32, 20, 40)
+        # fustat_1 <- c(1, 1, 1, 1, 1, 1, 0, 0, 0, 0)
+        # rx_1 <- c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
+        #
+        # futime_2 <- c(33, 28, 41, 48, 48, 25, 37, 48, 25, 43)
+        # fustat_2 <- c(1, 1, 1, 0, 0, 0, 0, 0, 0, 0)
+        # rx_2 <- c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
+        #
+        # futime <- c(futime_1, futime_2)
+        # fustat <- c(fustat_1, fustat_2)
+        # rx <- c(rx_1, rx_2)
+        #
+        # survdiff(formula = Surv(futime, fustat) ~ rx)
+        #
+        # Also check against another library which handle alternatives
+        # library(nph)
+        # logrank.test(futime, fustat, rx, alternative = "two.sided")
+        # res["test"]
+        [(
+              # https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_survival/BS704_Survival5.html
+              # uncensored, censored
+              [[8, 12, 26, 14, 21, 27], [8, 32, 20, 40]],
+              [[33, 28, 41], [48, 48, 25, 37, 48, 25, 43]],
+              # chi2, ["two-sided", "less", "greater"]
+              6.91598157449,
+              [0.008542873404, 0.9957285632979385, 0.004271436702061537]
+         ),
+         (
+              # https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_survival/BS704_Survival5.html
+              [[19, 6, 5, 4], [20, 19, 17, 14]],
+              [[16, 21, 7], [21, 15, 18, 18, 5]],
+              0.835004855038,
+              [0.3608293039, 0.8195853480676912, 0.1804146519323088]
+         ),
+         (
+              # Bland, Altman, "The logrank test", BMJ, 2004
+              # https://www.bmj.com/content/328/7447/1073.short
+              [[6, 13, 21, 30, 37, 38, 49, 50, 63, 79, 86, 98, 202, 219],
+               [31, 47, 80, 82, 82, 149]],
+              [[10, 10, 12, 13, 14, 15, 16, 17, 18, 20, 24, 24, 25, 28, 30,
+                33, 35, 37, 40, 40, 46, 48, 76, 81, 82, 91, 112, 181],
+               [34, 40, 70]],
+              7.49659416854,
+              [0.006181578637, 0.003090789318730882, 0.9969092106812691]
+         )]
+    )
+    def test_log_rank(self, x, y, statistic, pvalue):
+        x = stats.CensoredData(uncensored=x[0], right=x[1])
+        y = stats.CensoredData(uncensored=y[0], right=y[1])
+
+        for i, alternative in enumerate(["two-sided", "less", "greater"]):
+            res = stats.logrank(x=x, y=y, alternative=alternative)
+
+            # we return z and use the normal distribution while other framework
+            # return z**2. The p-value are directly comparable, but we have to
+            # square the statistic
+            assert_allclose(res.statistic**2, statistic, atol=1e-10)
+            assert_allclose(res.pvalue, pvalue[i], atol=1e-10)
+
+    def test_raises(self):
+        sample = stats.CensoredData([1, 2])
+
+        msg = r"`y` must be"
+        with pytest.raises(ValueError, match=msg):
+            stats.logrank(x=sample, y=[[1, 2]])
+
+        msg = r"`x` must be"
+        with pytest.raises(ValueError, match=msg):
+            stats.logrank(x=[[1, 2]], y=sample)