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798602c | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 | import numpy as np
from scipy.stats import chi2, norm
from scipy.stats import iqr, median_abs_deviation
# ============================================================
# Analytic Confidence Intervals
# ============================================================
def ci_deviation_analytic(
*,
data,
alpha,
estimator,
):
n = len(data)
if estimator == "Deviation (1 ddof)":
return _ci_std_chi2(data, alpha)
if estimator == "Range (bias corrected)":
return _ci_sigma_from_range(data, alpha)
if estimator == "IQR (bias corrected)":
return _ci_iqr_asymptotic(data, alpha)
if estimator == "MAD (bias corrected)":
return _ci_mad_asymptotic(data, alpha)
if estimator == "AAD (bias corrected)":
return _ci_aad_asymptotic(data, alpha)
raise ValueError(f"Unknown deviation estimator: {estimator}")
# -------------------------------
# χ² CI for σ (std, ddof=1)
# -------------------------------
def _ci_std_chi2(data, alpha):
n = len(data)
s = np.std(data, ddof=1)
num = s * np.sqrt(n - 1)
lo = num / np.sqrt(chi2.ppf(1 - alpha / 2, n - 1))
hi = num / np.sqrt(chi2.ppf(alpha / 2, n - 1))
return lo, hi
# -------------------------------
# Range-based CI (bias corrected)
# -------------------------------
def _ci_sigma_from_range(data, alpha):
n = len(data)
R = np.max(data) - np.min(data)
d2_n = d2(n)
d3_n = d3(n)
z = norm.ppf(1 - alpha / 2)
denom_lo = d2_n + z * d3_n
denom_hi = d2_n - z * d3_n
if denom_hi <= 0:
raise ValueError("Invalid configuration: denominator ≤ 0")
return R / denom_lo, R / denom_hi
# -------------------------------
# IQR (asymptotic)
# -------------------------------
def _ci_iqr_asymptotic(data, alpha):
n = len(data)
IQR = iqr(data)
w = 2 * norm.ppf(0.75)
k = np.sqrt(np.pi / (2 * np.exp(-norm.ppf(0.75) ** 2)))
z = norm.ppf(1 - alpha / 2)
return (
IQR / (w + z * k / np.sqrt(n)),
IQR / (w - z * k / np.sqrt(n)),
)
# -------------------------------
# MAD (asymptotic)
# -------------------------------
def _ci_mad_asymptotic(data, alpha):
n = len(data)
MAD = median_abs_deviation(data)
w = norm.ppf(0.75)
k = np.sqrt(np.pi / (8 * np.exp(-norm.ppf(0.75) ** 2)))
z = norm.ppf(1 - alpha / 2)
return (
MAD / (w + z * k / np.sqrt(n)),
MAD / (w - z * k / np.sqrt(n)),
)
# -------------------------------
# AAD (asymptotic)
# -------------------------------
def _ci_aad_asymptotic(data, alpha):
n = len(data)
AAD = np.mean(np.abs(data - np.mean(data)))
w = np.sqrt(2 / np.pi)
k = np.sqrt(1 - 2 / np.pi)
z = norm.ppf(1 - alpha / 2)
return (
AAD / (w + z * k / np.sqrt(n)),
AAD / (w - z * k / np.sqrt(n)),
)
# ============================================================
# Bootstrap Confidence Intervals
# ============================================================
def ci_deviation_bootstrap(
*,
data,
alpha,
B,
estimator,
):
"""
Bootstrap CI for deviation estimators.
"""
n = len(data)
if estimator == "Deviation (1 ddof)":
boot = np.array([
np.std(np.random.choice(data, n, replace=True), ddof=1)
for _ in range(B)
])
return np.quantile(boot, [alpha / 2, 1 - alpha / 2])
if estimator == "Range (bias corrected)":
boot = np.array([
np.max(b := np.random.choice(data, n, replace=True)) - np.min(b)
for _ in range(B)
])
return np.quantile(boot, [alpha / 2, 1 - alpha / 2]) / d2(n)
if estimator == "IQR (bias corrected)":
boot = np.array([
iqr(np.random.choice(data, n, replace=True))
for _ in range(B)
])
return np.quantile(boot, [alpha / 2, 1 - alpha / 2]) / (
2 * norm.ppf(0.75)
)
if estimator == "MAD (bias corrected)":
boot = np.array([
median_abs_deviation(np.random.choice(data, n, replace=True))
for _ in range(B)
])
return np.quantile(boot, [alpha / 2, 1 - alpha / 2]) / norm.ppf(0.75)
if estimator == "AAD (bias corrected)":
boot = np.array([
np.mean(np.abs(
(b := np.random.choice(data, n, replace=True))
- np.mean(b)
))
for _ in range(B)
])
return np.quantile(boot, [alpha / 2, 1 - alpha / 2]) * np.sqrt(np.pi / 2)
raise ValueError(f"Unknown deviation estimator: {estimator}")
# ============================================================
# Bias-correction constants (monolith-compatible)
# ============================================================
def d2(n):
table = {
2: 1.128, 3: 1.693, 4: 2.059, 5: 2.326, 6: 2.534,
7: 2.704, 8: 2.847, 9: 2.970, 10: 3.078,
11: 3.173, 12: 3.258, 13: 3.336, 14: 3.407,
15: 3.472, 16: 3.532, 17: 3.588, 18: 3.640,
19: 3.689, 20: 3.735, 21: 3.778, 22: 3.819,
23: 3.858, 24: 3.895, 25: 3.931,
}
return table[n]
def d3(n):
table = {
2: 0.852, 3: 0.888, 4: 0.880, 5: 0.864, 6: 0.848,
7: 0.833, 8: 0.820, 9: 0.808, 10: 0.797,
11: 0.787, 12: 0.778, 13: 0.770, 14: 0.763,
15: 0.756, 16: 0.750, 17: 0.744, 18: 0.739,
19: 0.734, 20: 0.729, 21: 0.724, 22: 0.720,
23: 0.716, 24: 0.712, 25: 0.708,
}
return table[n]
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