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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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rhettinger merged 1 commit into from
Jan 16, 2024
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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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12 changes: 5 additions & 7 deletions Doc/library/statistics.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -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
Expand All @@ -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]

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