From ec75bc8f023f5f58a1ec0ed44b5dbbb891fd36b7 Mon Sep 17 00:00:00 2001 From: Raymond Hettinger Date: Sat, 12 Aug 2023 21:26:59 -0500 Subject: [PATCH 1/7] Add subsection headings --- Doc/library/statistics.rst | 15 +++++++++++++++ 1 file changed, 15 insertions(+) diff --git a/Doc/library/statistics.rst b/Doc/library/statistics.rst index 395b324c860389..689b900a8a6b9d 100644 --- a/Doc/library/statistics.rst +++ b/Doc/library/statistics.rst @@ -922,6 +922,10 @@ of applications in statistics. :class:`NormalDist` Examples and Recipes ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Classic probability problems +**************************** + :class:`NormalDist` readily solves classic probability problems. For example, given `historical data for SAT exams @@ -947,6 +951,10 @@ Find the `quartiles `_ and `deciles >>> list(map(round, sat.quantiles(n=10))) [810, 896, 958, 1011, 1060, 1109, 1162, 1224, 1310] + +Monte Carlo inputs for simulations +********************************** + To estimate the distribution for a model than isn't easy to solve analytically, :class:`NormalDist` can generate input samples for a `Monte Carlo simulation `_: @@ -963,6 +971,9 @@ Carlo simulation `_: >>> quantiles(map(model, X, Y, Z)) # doctest: +SKIP [1.4591308524824727, 1.8035946855390597, 2.175091447274739] +Approximating binomial distributions +************************************ + Normal distributions can be used to approximate `Binomial distributions `_ when the sample size is large and when the probability of a successful @@ -1000,6 +1011,10 @@ probability that the Python room will stay within its capacity limits? >>> mean(trial() <= k for i in range(10_000)) 0.8398 + +Naive bayesian classifier +************************* + Normal distributions commonly arise in machine learning problems. 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kde_example.png + .. # This modelines must appear within the last ten lines of the file. kate: indent-width 3; remove-trailing-space on; replace-tabs on; encoding utf-8; From 840f9c3d85d7ae7b70bb5b9dade02b2e531640b8 Mon Sep 17 00:00:00 2001 From: Raymond Hettinger Date: Sat, 12 Aug 2023 22:53:43 -0500 Subject: [PATCH 3/7] Fix markup --- Doc/library/statistics.rst | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/Doc/library/statistics.rst b/Doc/library/statistics.rst index 081205355b50a4..52649f43a5a813 100644 --- a/Doc/library/statistics.rst +++ b/Doc/library/statistics.rst @@ -1075,7 +1075,7 @@ Kernel density estimation It is possible to estimate a continuous probability density function from a fixed number of discrete samples. -The basic idea is to smooth the data with using a kernel function +The basic idea is to smooth the data using a kernel function such as a normal distribution, triangular distribution, or uniform distribution. The degree of smoothing is controlled by a single parameter, ``h``, representing the variance of the kernel function. @@ -1093,19 +1093,19 @@ parameter, ``h``, representing the variance of the kernel function. return sum(kernel_h(x - x_i) for x_i in sample) / n return pdf -Wikipedia has an `example` +`Wikipedia has an example `_ -where we can use this recipe to generate and plot a probability -density function from a small sample: +where we can use the ``kde_normal()`` recipe to generate and plot +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) - >>> xarr = [i/100 for i in range(-750, 1100) + >>> xarr = [i/100 for i in range(-750, 1100)] >>> yarr = [f_hat(x) for x in xarr] -That data produces this plot: +That data produces this pdf plot: .. image:: kde_example.png From d37ed3bd185bddd4cdcc842da52dd9fed804a4a5 Mon Sep 17 00:00:00 2001 From: Raymond Hettinger Date: Sun, 13 Aug 2023 06:51:31 -0500 Subject: [PATCH 4/7] Link to common kernels --- Doc/library/statistics.rst | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) diff --git a/Doc/library/statistics.rst b/Doc/library/statistics.rst index 52649f43a5a813..11bf09ee57f1c7 100644 --- a/Doc/library/statistics.rst +++ b/Doc/library/statistics.rst @@ -1075,9 +1075,10 @@ Kernel density estimation It is possible to estimate a continuous probability density function 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. The degree of smoothing is controlled by a single +The basic idea is to smooth the data using a kernel function such as a +`normal distribution, triangular distribution, or uniform distribution +`_. +The degree of smoothing is controlled by a single parameter, ``h``, representing the variance of the kernel function. .. testcode:: From ebc25367ee9588bccdd03cf26092ae86006a0b10 Mon Sep 17 00:00:00 2001 From: Raymond Hettinger Date: Sun, 13 Aug 2023 07:25:02 -0500 Subject: [PATCH 5/7] Specifically reference xarr and yarr as inputs to the plot. --- Doc/library/statistics.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Doc/library/statistics.rst b/Doc/library/statistics.rst index 11bf09ee57f1c7..3f22f973e1b239 100644 --- a/Doc/library/statistics.rst +++ b/Doc/library/statistics.rst @@ -1106,7 +1106,7 @@ a probability density function estimated from a small sample: >>> xarr = [i/100 for i in range(-750, 1100)] >>> yarr = [f_hat(x) for x in xarr] -That data produces this pdf plot: +The points in ``xarr`` and ``yarr`` can be used to make this PDF plot: .. image:: kde_example.png From 4908a4f7f518893510da7cf349fcd6f386dc66f6 Mon Sep 17 00:00:00 2001 From: Raymond Hettinger Date: Sun, 13 Aug 2023 07:40:00 -0500 Subject: [PATCH 6/7] Add :alt: text for accessibility --- Doc/library/statistics.rst | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/Doc/library/statistics.rst b/Doc/library/statistics.rst index 3f22f973e1b239..a8ff5753c67782 100644 --- a/Doc/library/statistics.rst +++ b/Doc/library/statistics.rst @@ -1106,9 +1106,10 @@ a probability density function estimated from a small sample: >>> xarr = [i/100 for i in range(-750, 1100)] >>> yarr = [f_hat(x) for x in xarr] -The points in ``xarr`` and ``yarr`` can be used to make this PDF plot: +The points in ``xarr`` and ``yarr`` can be used to make a PDF plot: .. image:: kde_example.png + :alt: Scatter plot of the estimated probability density function. .. # This modelines must appear within the last ten lines of the file. From 7d5527cd5cb2c4314536c468f18b4e3b5e94d57c Mon Sep 17 00:00:00 2001 From: Raymond Hettinger Date: Sun, 13 Aug 2023 07:42:14 -0500 Subject: [PATCH 7/7] Include "kernel" in the link text. --- Doc/library/statistics.rst | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/Doc/library/statistics.rst b/Doc/library/statistics.rst index a8ff5753c67782..483ebea67f0c6d 100644 --- a/Doc/library/statistics.rst +++ b/Doc/library/statistics.rst @@ -1075,8 +1075,8 @@ Kernel density estimation It is possible to estimate a continuous probability density function 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 +The basic idea is to smooth the data using `a kernel function such as a +normal distribution, triangular distribution, or uniform distribution `_. The degree of smoothing is controlled by a single parameter, ``h``, representing the variance of the kernel function.