[Python-checkins] bpo-36018: Add another example for NormalDist() (#18191)
Raymond Hettinger
webhook-mailer at python.org
Sat Jan 25 23:21:22 EST 2020
https://github.com/python/cpython/commit/10355ed7f132ed10f1e0d8bd64ccb744b86b1cce
commit: 10355ed7f132ed10f1e0d8bd64ccb744b86b1cce
branch: master
author: Raymond Hettinger <rhettinger at users.noreply.github.com>
committer: GitHub <noreply at github.com>
date: 2020-01-25T20:21:17-08:00
summary:
bpo-36018: Add another example for NormalDist() (#18191)
files:
M Doc/library/statistics.rst
diff --git a/Doc/library/statistics.rst b/Doc/library/statistics.rst
index 4c7239c1895fb..09b02cabf21f8 100644
--- a/Doc/library/statistics.rst
+++ b/Doc/library/statistics.rst
@@ -772,6 +772,42 @@ Carlo simulation <https://en.wikipedia.org/wiki/Monte_Carlo_method>`_:
>>> quantiles(map(model, X, Y, Z)) # doctest: +SKIP
[1.4591308524824727, 1.8035946855390597, 2.175091447274739]
+Normal distributions can be used to approximate `Binomial
+distributions <http://mathworld.wolfram.com/BinomialDistribution.html>`_
+when the sample size is large and when the probability of a successful
+trial is near 50%.
+
+For example, an open source conference has 750 attendees and two rooms with a
+500 person capacity. There is a talk about Python and another about Ruby.
+In previous conferences, 65% of the attendees preferred to listen to Python
+talks. Assuming the population preferences haven't changed, what is the
+probability that the rooms will stay within their capacity limits?
+
+.. doctest::
+
+ >>> n = 750 # Sample size
+ >>> p = 0.65 # Preference for Python
+ >>> q = 1.0 - p # Preference for Ruby
+ >>> k = 500 # Room capacity
+
+ >>> # Approximation using the cumulative normal distribution
+ >>> from math import sqrt
+ >>> round(NormalDist(mu=n*p, sigma=sqrt(n*p*q)).cdf(k + 0.5), 4)
+ 0.8402
+
+ >>> # Solution using the cumulative binomial distribution
+ >>> from math import comb, fsum
+ >>> round(fsum(comb(n, r) * p**r * q**(n-r) for r in range(k+1)), 4)
+ 0.8402
+
+ >>> # Approximation using a simulation
+ >>> from random import seed, choices
+ >>> seed(8675309)
+ >>> def trial():
+ ... return choices(('Python', 'Ruby'), (p, q), k=n).count('Python')
+ >>> mean(trial() <= k for i in range(10_000))
+ 0.8398
+
Normal distributions commonly arise in machine learning problems.
Wikipedia has a `nice example of a Naive Bayesian Classifier
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