| // Copyright 2017 The Abseil Authors. | |
| // | |
| // Licensed under the Apache License, Version 2.0 (the "License"); | |
| // you may not use this file except in compliance with the License. | |
| // You may obtain a copy of the License at | |
| // | |
| // https://www.apache.org/licenses/LICENSE-2.0 | |
| // | |
| // Unless required by applicable law or agreed to in writing, software | |
| // distributed under the License is distributed on an "AS IS" BASIS, | |
| // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | |
| // See the License for the specific language governing permissions and | |
| // limitations under the License. | |
| // NOTE: The functions in this file are test only, and are should not be used in | |
| // non-test code. | |
| namespace absl { | |
| ABSL_NAMESPACE_BEGIN | |
| namespace random_internal { | |
| // http://webspace.ship.edu/pgmarr/Geo441/Lectures/Lec%205%20-%20Normality%20Testing.pdf | |
| // Compute the 1st to 4th standard moments: | |
| // mean, variance, skewness, and kurtosis. | |
| // http://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm | |
| struct DistributionMoments { | |
| size_t n = 0; | |
| double mean = 0.0; | |
| double variance = 0.0; | |
| double skewness = 0.0; | |
| double kurtosis = 0.0; | |
| }; | |
| DistributionMoments ComputeDistributionMoments( | |
| absl::Span<const double> data_points); | |
| std::ostream& operator<<(std::ostream& os, const DistributionMoments& moments); | |
| // Computes the Z-score for a set of data with the given distribution moments | |
| // compared against `expected_mean`. | |
| double ZScore(double expected_mean, const DistributionMoments& moments); | |
| // Returns the probability of success required for a single trial to ensure that | |
| // after `num_trials` trials, the probability of at least one failure is no more | |
| // than `p_fail`. | |
| double RequiredSuccessProbability(double p_fail, int num_trials); | |
| // Computes the maximum distance from the mean tolerable, for Z-Tests that are | |
| // expected to pass with `acceptance_probability`. Will terminate if the | |
| // resulting tolerance is zero (due to passing in 0.0 for | |
| // `acceptance_probability` or rounding errors). | |
| // | |
| // For example, | |
| // MaxErrorTolerance(0.001) = 0.0 | |
| // MaxErrorTolerance(0.5) = ~0.47 | |
| // MaxErrorTolerance(1.0) = inf | |
| double MaxErrorTolerance(double acceptance_probability); | |
| // Approximation to inverse of the Error Function in double precision. | |
| // (http://people.maths.ox.ac.uk/gilesm/files/gems_erfinv.pdf) | |
| double erfinv(double x); | |
| // Beta(p, q) = Gamma(p) * Gamma(q) / Gamma(p+q) | |
| double beta(double p, double q); | |
| // The inverse of the normal survival function. | |
| double InverseNormalSurvival(double x); | |
| // Returns whether actual is "near" expected, based on the bound. | |
| bool Near(absl::string_view msg, double actual, double expected, double bound); | |
| // Implements the incomplete regularized beta function, AS63, BETAIN. | |
| // https://www.jstor.org/stable/2346797 | |
| // | |
| // BetaIncomplete(x, p, q), where | |
| // `x` is the value of the upper limit | |
| // `p` is beta parameter p, `q` is beta parameter q. | |
| // | |
| // NOTE: This is a test-only function which is only accurate to within, at most, | |
| // 1e-13 of the actual value. | |
| // | |
| double BetaIncomplete(double x, double p, double q); | |
| // Implements the inverse of the incomplete regularized beta function, AS109, | |
| // XINBTA. | |
| // https://www.jstor.org/stable/2346798 | |
| // https://www.jstor.org/stable/2346887 | |
| // | |
| // BetaIncompleteInv(p, q, beta, alhpa) | |
| // `p` is beta parameter p, `q` is beta parameter q. | |
| // `alpha` is the value of the lower tail area. | |
| // | |
| // NOTE: This is a test-only function and, when successful, is only accurate to | |
| // within ~1e-6 of the actual value; there are some cases where it diverges from | |
| // the actual value by much more than that. The function uses Newton's method, | |
| // and thus the runtime is highly variable. | |
| double BetaIncompleteInv(double p, double q, double alpha); | |
| } // namespace random_internal | |
| ABSL_NAMESPACE_END | |
| } // namespace absl | |