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[3.12] Update KDE recipe to match the standard use of the h parameter (gh-113958) (#114098)

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Raymond Hettinger 2024-01-15 22:46:01 -06:00 • committed by GitHub
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12
Doc/library/statistics.rst
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@ -1094,17 +1094,15 @@ from a fixed number of discrete samples.
The basic idea is to smooth the data using `a kernel function such as a
normal distribution, triangular distribution, or uniform distribution
<https://en.wikipedia.org/wiki/Kernel_(statistics)#Kernel_functions_in_common_use>`_.
The degree of smoothing is controlled by a single
parameter, ``h``, representing the variance of the kernel function.
The degree of smoothing is controlled by a scaling parameter, ``h``,
which is called the *bandwidth*.
.. testcode::
import math
def kde_normal(sample, h):
"Create a continuous probability density function from a sample."
# Smooth the sample with a normal distribution of variance h.
kernel_h = NormalDist(0.0, math.sqrt(h)).pdf
# Smooth the sample with a normal distribution kernel scaled by h.
kernel_h = NormalDist(0.0, h).pdf
n = len(sample)
def pdf(x):
return sum(kernel_h(x - x_i) for x_i in sample) / n
@ -1118,7 +1116,7 @@ a probability density function estimated from a small sample:
.. doctest::
>>> sample = [-2.1, -1.3, -0.4, 1.9, 5.1, 6.2]
>>> f_hat = kde_normal(sample, h=2.25)
>>> f_hat = kde_normal(sample, h=1.5)
>>> xarr = [i/100 for i in range(-750, 1100)]
>>> yarr = [f_hat(x) for x in xarr]