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gh-115532: Minor tweaks to kde() (gh-117897)

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Raymond Hettinger 2024-04-15 10:08:21 -05:00 committed by GitHub
parent 10f1a2687a
commit 0823f43618
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2 changed files with 25 additions and 12 deletions
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3
Doc/library/statistics.rst
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@ -1163,7 +1163,7 @@ accurately approximated inverse cumulative distribution function.
.. testcode::
from random import choice, random, seed
from math import sqrt, log, pi, tan, asin
from math import sqrt, log, pi, tan, asin, cos, acos
from statistics import NormalDist
kernel_invcdfs = {
@ -1172,6 +1172,7 @@ accurately approximated inverse cumulative distribution function.
'sigmoid': lambda p: log(tan(p * pi/2)),
'rectangular': lambda p: 2*p - 1,
'triangular': lambda p: sqrt(2*p) - 1 if p < 0.5 else 1 - sqrt(2 - 2*p),
'parabolic': lambda p: 2 * cos((acos(2*p-1) + pi) / 3),
'cosine': lambda p: 2*asin(2*p - 1)/pi,
}

34
Lib/statistics.py
View File

@ -919,13 +919,13 @@ def kde(data, h, kernel='normal', *, cumulative=False):
sqrt2pi = sqrt(2 * pi)
sqrt2 = sqrt(2)
K = lambda t: exp(-1/2 * t * t) / sqrt2pi
I = lambda t: 1/2 * (1.0 + erf(t / sqrt2))
W = lambda t: 1/2 * (1.0 + erf(t / sqrt2))
support = None
case 'logistic':
# 1.0 / (exp(t) + 2.0 + exp(-t))
K = lambda t: 1/2 / (1.0 + cosh(t))
I = lambda t: 1.0 - 1.0 / (exp(t) + 1.0)
W = lambda t: 1.0 - 1.0 / (exp(t) + 1.0)
support = None
case 'sigmoid':
@ -933,39 +933,39 @@ def kde(data, h, kernel='normal', *, cumulative=False):
c1 = 1 / pi
c2 = 2 / pi
K = lambda t: c1 / cosh(t)
I = lambda t: c2 * atan(exp(t))
W = lambda t: c2 * atan(exp(t))
support = None
case 'rectangular' | 'uniform':
K = lambda t: 1/2
I = lambda t: 1/2 * t + 1/2
W = lambda t: 1/2 * t + 1/2
support = 1.0
case 'triangular':
K = lambda t: 1.0 - abs(t)
I = lambda t: t*t * (1/2 if t < 0.0 else -1/2) + t + 1/2
W = lambda t: t*t * (1/2 if t < 0.0 else -1/2) + t + 1/2
support = 1.0
case 'parabolic' | 'epanechnikov':
K = lambda t: 3/4 * (1.0 - t * t)
I = lambda t: -1/4 * t**3 + 3/4 * t + 1/2
W = lambda t: -1/4 * t**3 + 3/4 * t + 1/2
support = 1.0
case 'quartic' | 'biweight':
K = lambda t: 15/16 * (1.0 - t * t) ** 2
I = lambda t: 3/16 * t**5 - 5/8 * t**3 + 15/16 * t + 1/2
W = lambda t: 3/16 * t**5 - 5/8 * t**3 + 15/16 * t + 1/2
support = 1.0
case 'triweight':
K = lambda t: 35/32 * (1.0 - t * t) ** 3
I = lambda t: 35/32 * (-1/7*t**7 + 3/5*t**5 - t**3 + t) + 1/2
W = lambda t: 35/32 * (-1/7*t**7 + 3/5*t**5 - t**3 + t) + 1/2
support = 1.0
case 'cosine':
c1 = pi / 4
c2 = pi / 2
K = lambda t: c1 * cos(c2 * t)
I = lambda t: 1/2 * sin(c2 * t) + 1/2
W = lambda t: 1/2 * sin(c2 * t) + 1/2
support = 1.0
case _:
@ -974,10 +974,14 @@ def kde(data, h, kernel='normal', *, cumulative=False):
if support is None:
def pdf(x):
n = len(data)
return sum(K((x - x_i) / h) for x_i in data) / (n * h)
def cdf(x):
return sum(I((x - x_i) / h) for x_i in data) / n
n = len(data)
return sum(W((x - x_i) / h) for x_i in data) / n
else:
@ -985,16 +989,24 @@ def kde(data, h, kernel='normal', *, cumulative=False):
bandwidth = h * support
def pdf(x):
nonlocal n, sample
if len(data) != n:
sample = sorted(data)
n = len(data)
i = bisect_left(sample, x - bandwidth)
j = bisect_right(sample, x + bandwidth)
supported = sample[i : j]
return sum(K((x - x_i) / h) for x_i in supported) / (n * h)
def cdf(x):
nonlocal n, sample
if len(data) != n:
sample = sorted(data)
n = len(data)
i = bisect_left(sample, x - bandwidth)
j = bisect_right(sample, x + bandwidth)
supported = sample[i : j]
return sum((I((x - x_i) / h) for x_i in supported), i) / n
return sum((W((x - x_i) / h) for x_i in supported), i) / n
if cumulative:
cdf.__doc__ = f'CDF estimate with {h=!r} and {kernel=!r}'