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Minor accuracy improvements in statistics #157380

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Merged
rhettinger merged 4 commits into from
Sep 13, 2026
+15 −17
Merged

Minor accuracy improvements in statistics #157380

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60ab407
Apply new sinpi/cospi/tanpi functions
rhettinger Sep 12, 2026
c4a0eea
Use more accurate sqrt(2*pi)
rhettinger Sep 12, 2026
4c18bca
Merge branch 'main' into stats_cospi_sinpi
rhettinger Sep 13, 2026
dd51688
Merge branch 'main' into stats_cospi_sinpi
rhettinger Sep 13, 2026
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32 changes: 15 additions & 17 deletions Lib/statistics.py
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Original file line number Diff line number Diff line change
Expand Up @@ -138,14 +138,15 @@
from decimal import Decimal
from itertools import compress, count, groupby, repeat
from bisect import bisect_left, bisect_right
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 math import hypot, sqrt, fabs, exp, erfc, log, fsum, sumprod
from math import isfinite, isinf, pi, sin, cosh
from math import sinpi, cospi, tanpi, asinpi, acospi, atanpi
from functools import reduce
from operator import itemgetter
from collections import Counter, namedtuple, defaultdict

_SQRT2 = sqrt(2.0)
_SQRT2PI = sqrt(tau)
_SQRT2PI = float.fromhex('0x1.40d931ff62706p+1') # Correctly rounded sqrt(2*pi)
_random = random

## Exceptions ##############################################################
Expand Down Expand Up @@ -820,8 +821,8 @@ def deco(builder):

@register('normal', 'gauss')
def normal_kernel():
sqrt2pi = sqrt(2 * pi)
neg_sqrt2 = -sqrt(2)
sqrt2pi = _SQRT2PI
neg_sqrt2 = -_SQRT2
pdf = lambda t: exp(-1/2 * t * t) / sqrt2pi
cdf = lambda t: 1/2 * erfc(t / neg_sqrt2)
invcdf = lambda t: _normal_dist_inv_cdf(t, 0.0, 1.0)
Expand All @@ -840,12 +841,10 @@ def logistic_kernel():
@register('sigmoid')
def sigmoid_kernel():
# (2/pi) / (exp(t) + exp(-t))
c1 = 1 / pi
c2 = 2 / pi
c3 = pi / 2
pdf = lambda t: c1 / cosh(t)
cdf = lambda t: c2 * atan(exp(t))
invcdf = lambda p: log(tan(p * c3))
recip_pi = 1 / pi
pdf = lambda t: recip_pi / cosh(t)
cdf = lambda t: 2.0 * atanpi(exp(t))
invcdf = lambda p: log(tanpi(p * 0.5))
support = None
return pdf, cdf, invcdf, support

Expand All @@ -869,7 +868,7 @@ def triangular_kernel():
def parabolic_kernel():
pdf = lambda t: 3/4 * (1.0 - t * t)
cdf = lambda t: sumprod((-1/4, 3/4, 1/2), (t**3, t, 1.0))
invcdf = lambda p: 2.0 * cos((acos(2.0*p - 1.0) + pi) / 3.0)
invcdf = lambda p: 2.0 * cospi((acospi(2.0 * p - 1.0) + 1.0) / 3.0)
support = 1.0
return pdf, cdf, invcdf, support

Expand Down Expand Up @@ -906,7 +905,7 @@ def _triweight_invcdf_estimate(p):
sign, p = (1.0, p) if p <= 1/2 else (-1.0, 1.0 - p)
x = (2.0 * p) ** 0.3400218741872791 - 1.0
if 0.00001 < p < 0.499:
x -= 0.033 * sin(1.07 * tau * (p - 0.035))
x -= 0.033 * sinpi(2.14 * (p - 0.035))
return x * sign

@register('triweight')
Expand All @@ -921,10 +920,9 @@ def triweight_kernel():
@register('cosine')
def cosine_kernel():
c1 = pi / 4
c2 = pi / 2
pdf = lambda t: c1 * cos(c2 * t)
cdf = lambda t: 1/2 * sin(c2 * t) + 1/2
invcdf = lambda p: 2.0 * asin(2.0 * p - 1.0) / pi
pdf = lambda t: c1 * cospi(0.5 * t)
cdf = lambda t: 1/2 * sinpi(0.5 * t) + 1/2
invcdf = lambda p: 2.0 * asinpi(2.0 * p - 1.0)
support = 1.0
return pdf, cdf, invcdf, support

Expand Down
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