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gh-132893: More accurate CDF computation (gh-132895)

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Raymond Hettinger 2025-04-25 00:34:55 -05:00 • committed by GitHub
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commit 63da5cc150
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2 changed files with 6 additions and 4 deletions
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9
Lib/statistics.py
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@ -138,7 +138,7 @@ from fractions import Fraction
from decimal import Decimal
from itertools import count, groupby, repeat
from bisect import bisect_left, bisect_right
from math import hypot, sqrt, fabs, exp, erf, tau, log, fsum, sumprod
from math import hypot, sqrt, fabs, exp, erfc, tau, log, fsum, sumprod
from math import isfinite, isinf, pi, cos, sin, tan, cosh, asin, atan, acos
from functools import reduce
from operator import itemgetter
@ -811,8 +811,9 @@ def register(*kernels):
def normal_kernel():
sqrt2pi = sqrt(2 * pi)
sqrt2 = sqrt(2)
neg_sqrt2 = -sqrt2
pdf = lambda t: exp(-1/2 * t * t) / sqrt2pi
cdf = lambda t: 1/2 * (1.0 + erf(t / sqrt2))
cdf = lambda t: 1/2 * erfc(t / neg_sqrt2)
invcdf = lambda t: _normal_dist_inv_cdf(t, 0.0, 1.0)
support = None
return pdf, cdf, invcdf, support
@ -1257,7 +1258,7 @@ class NormalDist:
"Cumulative distribution function. P(X <= x)"
if not self._sigma:
raise StatisticsError('cdf() not defined when sigma is zero')
return 0.5 * (1.0 + erf((x - self._mu) / (self._sigma * _SQRT2)))
return 0.5 * erfc((self._mu - x) / (self._sigma * _SQRT2))
def inv_cdf(self, p):
"""Inverse cumulative distribution function. x : P(X <= x) = p
@ -1311,7 +1312,7 @@ class NormalDist:
dv = Y_var - X_var
dm = fabs(Y._mu - X._mu)
if not dv:
return 1.0 - erf(dm / (2.0 * X._sigma * _SQRT2))
return erfc(dm / (2.0 * X._sigma * _SQRT2))
a = X._mu * Y_var - Y._mu * X_var
b = X._sigma * Y._sigma * sqrt(dm * dm + dv * log(Y_var / X_var))
x1 = (a + b) / dv

1
Misc/NEWS.d/next/Library/2025-04-24-21-22-46.gh-issue-132893.KFuxZ2.rst Normal file
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@ -0,0 +1 @@
Improved the accuracy of ``statistics.NormalDist.cdf`` for negative inputs.