https://github.com/python/cpython/commit/63da5cc1504f066b31374027f637b4b021445d6b
commit: 63da5cc1504f066b31374027f637b4b021445d6b
branch: main
author: Raymond Hettinger <rhettin...@users.noreply.github.com>
committer: rhettinger <rhettin...@users.noreply.github.com>
date: 2025-04-25T00:34:55-05:00
summary:
gh-132893: More accurate CDF computation (gh-132895)
files:
A Misc/NEWS.d/next/Library/2025-04-24-21-22-46.gh-issue-132893.KFuxZ2.rst
M Lib/statistics.py
diff --git a/Lib/statistics.py b/Lib/statistics.py
index e2b59267f04f68..9dcb20d2a485eb 100644
--- a/Lib/statistics.py
+++ b/Lib/statistics.py
@@ -138,7 +138,7 @@
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 deco(builder):
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 @@ def cdf(self, x):
"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 @@ def overlap(self, other):
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
diff --git
a/Misc/NEWS.d/next/Library/2025-04-24-21-22-46.gh-issue-132893.KFuxZ2.rst
b/Misc/NEWS.d/next/Library/2025-04-24-21-22-46.gh-issue-132893.KFuxZ2.rst
new file mode 100644
index 00000000000000..1ef651188e04bc
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2025-04-24-21-22-46.gh-issue-132893.KFuxZ2.rst
@@ -0,0 +1 @@
+Improved the accuracy of ``statistics.NormalDist.cdf`` for negative inputs.
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