[Python-checkins] bpo-36018: Add the NormalDist class to the statistics module (GH-11973)
Raymond Hettinger
webhook-mailer at python.org
Sat Feb 23 17:44:12 EST 2019
https://github.com/python/cpython/commit/11c79531655a4aa3f82c20ff562ac571f40040cc
commit: 11c79531655a4aa3f82c20ff562ac571f40040cc
branch: master
author: Raymond Hettinger <rhettinger at users.noreply.github.com>
committer: GitHub <noreply at github.com>
date: 2019-02-23T14:44:07-08:00
summary:
bpo-36018: Add the NormalDist class to the statistics module (GH-11973)
files:
A Misc/NEWS.d/next/Library/2019-02-21-15-47-00.bpo-36018.qt7QUe.rst
M Doc/library/statistics.rst
M Doc/whatsnew/3.8.rst
M Lib/statistics.py
M Lib/test/test_statistics.py
diff --git a/Doc/library/statistics.rst b/Doc/library/statistics.rst
index 20a2c1cb13e1..c1be295cbf95 100644
--- a/Doc/library/statistics.rst
+++ b/Doc/library/statistics.rst
@@ -467,6 +467,201 @@ A single exception is defined:
Subclass of :exc:`ValueError` for statistics-related exceptions.
+
+:class:`NormalDist` objects
+===========================
+
+A :class:`NormalDist` is a a composite class that treats the mean and standard
+deviation of data measurements as a single entity. It is a tool for creating
+and manipulating normal distributions of a random variable.
+
+Normal distributions arise from the `Central Limit Theorem
+<https://en.wikipedia.org/wiki/Central_limit_theorem>`_ and have a wide range
+of applications in statistics, including simulations and hypothesis testing.
+
+.. class:: NormalDist(mu=0.0, sigma=1.0)
+
+ Returns a new *NormalDist* object where *mu* represents the `arithmetic
+ mean <https://en.wikipedia.org/wiki/Arithmetic_mean>`_ of data and *sigma*
+ represents the `standard deviation
+ <https://en.wikipedia.org/wiki/Standard_deviation>`_ of the data.
+
+ If *sigma* is negative, raises :exc:`StatisticsError`.
+
+ .. attribute:: mu
+
+ The mean of a normal distribution.
+
+ .. attribute:: sigma
+
+ The standard deviation of a normal distribution.
+
+ .. attribute:: variance
+
+ A read-only property representing the `variance
+ <https://en.wikipedia.org/wiki/Variance>`_ of a normal
+ distribution. Equal to the square of the standard deviation.
+
+ .. classmethod:: NormalDist.from_samples(data)
+
+ Class method that makes a normal distribution instance
+ from sample data. The *data* can be any :term:`iterable`
+ and should consist of values that can be converted to type
+ :class:`float`.
+
+ If *data* does not contain at least two elements, raises
+ :exc:`StatisticsError` because it takes at least one point to estimate
+ a central value and at least two points to estimate dispersion.
+
+ .. method:: NormalDist.samples(n, seed=None)
+
+ Generates *n* random samples for a given mean and standard deviation.
+ Returns a :class:`list` of :class:`float` values.
+
+ If *seed* is given, creates a new instance of the underlying random
+ number generator. This is useful for creating reproducible results,
+ even in a multi-threading context.
+
+ .. method:: NormalDist.pdf(x)
+
+ Using a `probability density function (pdf)
+ <https://en.wikipedia.org/wiki/Probability_density_function>`_,
+ compute the relative likelihood that a random sample *X* will be near
+ the given value *x*. Mathematically, it is the ratio ``P(x <= X <
+ x+dx) / dx``.
+
+ Note the relative likelihood of *x* can be greater than `1.0`. The
+ probability for a specific point on a continuous distribution is `0.0`,
+ so the :func:`pdf` is used instead. It gives the probability of a
+ sample occurring in a narrow range around *x* and then dividing that
+ probability by the width of the range (hence the word "density").
+
+ .. method:: NormalDist.cdf(x)
+
+ Using a `cumulative distribution function (cdf)
+ <https://en.wikipedia.org/wiki/Cumulative_distribution_function>`_,
+ compute the probability that a random sample *X* will be less than or
+ equal to *x*. Mathematically, it is written ``P(X <= x)``.
+
+ Instances of :class:`NormalDist` support addition, subtraction,
+ multiplication and division by a constant. These operations
+ are used for translation and scaling. For example:
+
+ .. doctest::
+
+ >>> temperature_february = NormalDist(5, 2.5) # Celsius
+ >>> temperature_february * (9/5) + 32 # Fahrenheit
+ NormalDist(mu=41.0, sigma=4.5)
+
+ Dividing a constant by an instance of :class:`NormalDist` is not supported.
+
+ Since normal distributions arise from additive effects of independent
+ variables, it is possible to `add and subtract two normally distributed
+ random variables
+ <https://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables>`_
+ represented as instances of :class:`NormalDist`. For example:
+
+ .. doctest::
+
+ >>> birth_weights = NormalDist.from_samples([2.5, 3.1, 2.1, 2.4, 2.7, 3.5])
+ >>> drug_effects = NormalDist(0.4, 0.15)
+ >>> combined = birth_weights + drug_effects
+ >>> f'mu={combined.mu :.1f} sigma={combined.sigma :.1f}'
+ 'mu=3.1 sigma=0.5'
+
+ .. versionadded:: 3.8
+
+
+:class:`NormalDist` Examples and Recipes
+----------------------------------------
+
+A :class:`NormalDist` readily solves classic probability problems.
+
+For example, given `historical data for SAT exams
+<https://blog.prepscholar.com/sat-standard-deviation>`_ showing that scores
+are normally distributed with a mean of 1060 and standard deviation of 192,
+determine the percentage of students with scores between 1100 and 1200:
+
+.. doctest::
+
+ >>> sat = NormalDist(1060, 195)
+ >>> fraction = sat.cdf(1200) - sat.cdf(1100)
+ >>> f'{fraction * 100 :.1f}% score between 1100 and 1200'
+ '18.2% score between 1100 and 1200'
+
+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 <https://en.wikipedia.org/wiki/Monte_Carlo_method>`_ of the
+model:
+
+.. doctest::
+
+ >>> n = 100_000
+ >>> X = NormalDist(350, 15).samples(n)
+ >>> Y = NormalDist(47, 17).samples(n)
+ >>> Z = NormalDist(62, 6).samples(n)
+ >>> model_simulation = [x * y / z for x, y, z in zip(X, Y, Z)]
+ >>> NormalDist.from_samples(model_simulation) # doctest: +SKIP
+ NormalDist(mu=267.6516398754636, sigma=101.357284306067)
+
+Normal distributions commonly arise in machine learning problems.
+
+Wikipedia has a `nice example with a Naive Bayesian Classifier
+<https://en.wikipedia.org/wiki/Naive_Bayes_classifier>`_. The challenge
+is to guess a person's gender from measurements of normally distributed
+features including height, weight, and foot size.
+
+The `prior probability <https://en.wikipedia.org/wiki/Prior_probability>`_ of
+being male or female is 50%:
+
+.. doctest::
+
+ >>> prior_male = 0.5
+ >>> prior_female = 0.5
+
+We also have a training dataset with measurements for eight people. These
+measurements are assumed to be normally distributed, so we summarize the data
+with :class:`NormalDist`:
+
+.. doctest::
+
+ >>> height_male = NormalDist.from_samples([6, 5.92, 5.58, 5.92])
+ >>> height_female = NormalDist.from_samples([5, 5.5, 5.42, 5.75])
+ >>> weight_male = NormalDist.from_samples([180, 190, 170, 165])
+ >>> weight_female = NormalDist.from_samples([100, 150, 130, 150])
+ >>> foot_size_male = NormalDist.from_samples([12, 11, 12, 10])
+ >>> foot_size_female = NormalDist.from_samples([6, 8, 7, 9])
+
+We observe a new person whose feature measurements are known but whose gender
+is unknown:
+
+.. doctest::
+
+ >>> ht = 6.0 # height
+ >>> wt = 130 # weight
+ >>> fs = 8 # foot size
+
+The posterior is the product of the prior times each likelihood of a
+feature measurement given the gender:
+
+.. doctest::
+
+ >>> posterior_male = (prior_male * height_male.pdf(ht) *
+ ... weight_male.pdf(wt) * foot_size_male.pdf(fs))
+
+ >>> posterior_female = (prior_female * height_female.pdf(ht) *
+ ... weight_female.pdf(wt) * foot_size_female.pdf(fs))
+
+The final prediction is awarded to the largest posterior -- this is known as
+the `maximum a posteriori
+<https://en.wikipedia.org/wiki/Maximum_a_posteriori_estimation>`_ or MAP:
+
+.. doctest::
+
+ >>> 'male' if posterior_male > posterior_female else 'female'
+ 'female'
+
+
..
# 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;
diff --git a/Doc/whatsnew/3.8.rst b/Doc/whatsnew/3.8.rst
index f21175a5a2a8..68a4457106bb 100644
--- a/Doc/whatsnew/3.8.rst
+++ b/Doc/whatsnew/3.8.rst
@@ -278,6 +278,32 @@ Added :func:`statistics.fmean` as a faster, floating point variant of
:func:`statistics.mean()`. (Contributed by Raymond Hettinger and
Steven D'Aprano in :issue:`35904`.)
+Added :class:`statistics.NormalDist`, a tool for creating
+and manipulating normal distributions of a random variable.
+(Contributed by Raymond Hettinger in :issue:`36018`.)
+
+::
+
+ >>> temperature_feb = NormalDist.from_samples([4, 12, -3, 2, 7, 14])
+ >>> temperature_feb
+ NormalDist(mu=6.0, sigma=6.356099432828281)
+
+ >>> temperature_feb.cdf(3) # Chance of being under 3 degrees
+ 0.3184678262814532
+ >>> # Relative chance of being 7 degrees versus 10 degrees
+ >>> temperature_feb.pdf(7) / temperature_feb.pdf(10)
+ 1.2039930378537762
+
+ >>> el_nino = NormalDist(4, 2.5)
+ >>> temperature_feb += el_nino # Add in a climate effect
+ >>> temperature_feb
+ NormalDist(mu=10.0, sigma=6.830080526611674)
+
+ >>> temperature_feb * (9/5) + 32 # Convert to Fahrenheit
+ NormalDist(mu=50.0, sigma=12.294144947901014)
+ >>> temperature_feb.samples(3) # Generate random samples
+ [7.672102882379219, 12.000027119750287, 4.647488369766392]
+
tokenize
--------
diff --git a/Lib/statistics.py b/Lib/statistics.py
index 8ecb906d8699..a73001ac554c 100644
--- a/Lib/statistics.py
+++ b/Lib/statistics.py
@@ -76,7 +76,7 @@
"""
-__all__ = [ 'StatisticsError',
+__all__ = [ 'StatisticsError', 'NormalDist',
'pstdev', 'pvariance', 'stdev', 'variance',
'median', 'median_low', 'median_high', 'median_grouped',
'mean', 'mode', 'harmonic_mean', 'fmean',
@@ -85,11 +85,13 @@
import collections
import math
import numbers
+import random
from fractions import Fraction
from decimal import Decimal
from itertools import groupby
from bisect import bisect_left, bisect_right
+from math import hypot, sqrt, fabs, exp, erf, tau
@@ -694,3 +696,155 @@ def pstdev(data, mu=None):
return var.sqrt()
except AttributeError:
return math.sqrt(var)
+
+## Normal Distribution #####################################################
+
+class NormalDist:
+ 'Normal distribution of a random variable'
+ # https://en.wikipedia.org/wiki/Normal_distribution
+ # https://en.wikipedia.org/wiki/Variance#Properties
+
+ __slots__ = ('mu', 'sigma')
+
+ def __init__(self, mu=0.0, sigma=1.0):
+ 'NormalDist where mu is the mean and sigma is the standard deviation'
+ if sigma < 0.0:
+ raise StatisticsError('sigma must be non-negative')
+ self.mu = mu
+ self.sigma = sigma
+
+ @classmethod
+ def from_samples(cls, data):
+ 'Make a normal distribution instance from sample data'
+ if not isinstance(data, (list, tuple)):
+ data = list(data)
+ xbar = fmean(data)
+ return cls(xbar, stdev(data, xbar))
+
+ def samples(self, n, seed=None):
+ 'Generate *n* samples for a given mean and standard deviation'
+ gauss = random.gauss if seed is None else random.Random(seed).gauss
+ mu, sigma = self.mu, self.sigma
+ return [gauss(mu, sigma) for i in range(n)]
+
+ def pdf(self, x):
+ 'Probability density function: P(x <= X < x+dx) / dx'
+ variance = self.sigma ** 2.0
+ if not variance:
+ raise StatisticsError('pdf() not defined when sigma is zero')
+ return exp((x - self.mu)**2.0 / (-2.0*variance)) / sqrt(tau * variance)
+
+ def cdf(self, x):
+ 'Cumulative density function: P(X <= x)'
+ if not self.sigma:
+ raise StatisticsError('cdf() not defined when sigma is zero')
+ return 0.5 * (1.0 + erf((x - self.mu) / (self.sigma * sqrt(2.0))))
+
+ @property
+ def variance(self):
+ 'Square of the standard deviation'
+ return self.sigma ** 2.0
+
+ def __add__(x1, x2):
+ if isinstance(x2, NormalDist):
+ return NormalDist(x1.mu + x2.mu, hypot(x1.sigma, x2.sigma))
+ return NormalDist(x1.mu + x2, x1.sigma)
+
+ def __sub__(x1, x2):
+ if isinstance(x2, NormalDist):
+ return NormalDist(x1.mu - x2.mu, hypot(x1.sigma, x2.sigma))
+ return NormalDist(x1.mu - x2, x1.sigma)
+
+ def __mul__(x1, x2):
+ return NormalDist(x1.mu * x2, x1.sigma * fabs(x2))
+
+ def __truediv__(x1, x2):
+ return NormalDist(x1.mu / x2, x1.sigma / fabs(x2))
+
+ def __pos__(x1):
+ return x1
+
+ def __neg__(x1):
+ return NormalDist(-x1.mu, x1.sigma)
+
+ __radd__ = __add__
+
+ def __rsub__(x1, x2):
+ return -(x1 - x2)
+
+ __rmul__ = __mul__
+
+ def __eq__(x1, x2):
+ if not isinstance(x2, NormalDist):
+ return NotImplemented
+ return (x1.mu, x2.sigma) == (x2.mu, x2.sigma)
+
+ def __repr__(self):
+ return f'{type(self).__name__}(mu={self.mu!r}, sigma={self.sigma!r})'
+
+
+if __name__ == '__main__':
+
+ # Show math operations computed analytically in comparsion
+ # to a monte carlo simulation of the same operations
+
+ from math import isclose
+ from operator import add, sub, mul, truediv
+ from itertools import repeat
+
+ g1 = NormalDist(10, 20)
+ g2 = NormalDist(-5, 25)
+
+ # Test scaling by a constant
+ assert (g1 * 5 / 5).mu == g1.mu
+ assert (g1 * 5 / 5).sigma == g1.sigma
+
+ n = 100_000
+ G1 = g1.samples(n)
+ G2 = g2.samples(n)
+
+ for func in (add, sub):
+ print(f'\nTest {func.__name__} with another NormalDist:')
+ print(func(g1, g2))
+ print(NormalDist.from_samples(map(func, G1, G2)))
+
+ const = 11
+ for func in (add, sub, mul, truediv):
+ print(f'\nTest {func.__name__} with a constant:')
+ print(func(g1, const))
+ print(NormalDist.from_samples(map(func, G1, repeat(const))))
+
+ const = 19
+ for func in (add, sub, mul):
+ print(f'\nTest constant with {func.__name__}:')
+ print(func(const, g1))
+ print(NormalDist.from_samples(map(func, repeat(const), G1)))
+
+ def assert_close(G1, G2):
+ assert isclose(G1.mu, G1.mu, rel_tol=0.01), (G1, G2)
+ assert isclose(G1.sigma, G2.sigma, rel_tol=0.01), (G1, G2)
+
+ X = NormalDist(-105, 73)
+ Y = NormalDist(31, 47)
+ s = 32.75
+ n = 100_000
+
+ S = NormalDist.from_samples([x + s for x in X.samples(n)])
+ assert_close(X + s, S)
+
+ S = NormalDist.from_samples([x - s for x in X.samples(n)])
+ assert_close(X - s, S)
+
+ S = NormalDist.from_samples([x * s for x in X.samples(n)])
+ assert_close(X * s, S)
+
+ S = NormalDist.from_samples([x / s for x in X.samples(n)])
+ assert_close(X / s, S)
+
+ S = NormalDist.from_samples([x + y for x, y in zip(X.samples(n),
+ Y.samples(n))])
+ assert_close(X + Y, S)
+
+ S = NormalDist.from_samples([x - y for x, y in zip(X.samples(n),
+ Y.samples(n))])
+ assert_close(X - Y, S)
diff --git a/Lib/test/test_statistics.py b/Lib/test/test_statistics.py
index e35144677ad5..a65fbe8dd259 100644
--- a/Lib/test/test_statistics.py
+++ b/Lib/test/test_statistics.py
@@ -5,9 +5,11 @@
import collections
import collections.abc
+import copy
import decimal
import doctest
import math
+import pickle
import random
import sys
import unittest
@@ -2025,6 +2027,181 @@ def test_compare_to_variance(self):
expected = math.sqrt(statistics.variance(data))
self.assertEqual(self.func(data), expected)
+class TestNormalDist(unittest.TestCase):
+
+ def test_slots(self):
+ nd = statistics.NormalDist(300, 23)
+ with self.assertRaises(TypeError):
+ vars(nd)
+ self.assertEqual(nd.__slots__, ('mu', 'sigma'))
+
+ def test_instantiation_and_attributes(self):
+ nd = statistics.NormalDist(500, 17)
+ self.assertEqual(nd.mu, 500)
+ self.assertEqual(nd.sigma, 17)
+ self.assertEqual(nd.variance, 17**2)
+
+ # default arguments
+ nd = statistics.NormalDist()
+ self.assertEqual(nd.mu, 0)
+ self.assertEqual(nd.sigma, 1)
+ self.assertEqual(nd.variance, 1**2)
+
+ # error case: negative sigma
+ with self.assertRaises(statistics.StatisticsError):
+ statistics.NormalDist(500, -10)
+
+ def test_alternative_constructor(self):
+ NormalDist = statistics.NormalDist
+ data = [96, 107, 90, 92, 110]
+ # list input
+ self.assertEqual(NormalDist.from_samples(data), NormalDist(99, 9))
+ # tuple input
+ self.assertEqual(NormalDist.from_samples(tuple(data)), NormalDist(99, 9))
+ # iterator input
+ self.assertEqual(NormalDist.from_samples(iter(data)), NormalDist(99, 9))
+ # error cases
+ with self.assertRaises(statistics.StatisticsError):
+ NormalDist.from_samples([]) # empty input
+ with self.assertRaises(statistics.StatisticsError):
+ NormalDist.from_samples([10]) # only one input
+
+ def test_sample_generation(self):
+ NormalDist = statistics.NormalDist
+ mu, sigma = 10_000, 3.0
+ X = NormalDist(mu, sigma)
+ n = 1_000
+ data = X.samples(n)
+ self.assertEqual(len(data), n)
+ self.assertEqual(set(map(type, data)), {float})
+ # mean(data) expected to fall within 8 standard deviations
+ xbar = statistics.mean(data)
+ self.assertTrue(mu - sigma*8 <= xbar <= mu + sigma*8)
+
+ # verify that seeding makes reproducible sequences
+ n = 100
+ data1 = X.samples(n, seed='happiness and joy')
+ data2 = X.samples(n, seed='trouble and despair')
+ data3 = X.samples(n, seed='happiness and joy')
+ data4 = X.samples(n, seed='trouble and despair')
+ self.assertEqual(data1, data3)
+ self.assertEqual(data2, data4)
+ self.assertNotEqual(data1, data2)
+
+ # verify that subclass type is honored
+ class NewNormalDist(NormalDist):
+ pass
+ nnd = NewNormalDist(200, 5)
+ self.assertEqual(type(nnd), NewNormalDist)
+
+ def test_pdf(self):
+ NormalDist = statistics.NormalDist
+ X = NormalDist(100, 15)
+ # Verify peak around center
+ self.assertLess(X.pdf(99), X.pdf(100))
+ self.assertLess(X.pdf(101), X.pdf(100))
+ # Test symmetry
+ self.assertAlmostEqual(X.pdf(99), X.pdf(101))
+ self.assertAlmostEqual(X.pdf(98), X.pdf(102))
+ self.assertAlmostEqual(X.pdf(97), X.pdf(103))
+ # Test vs CDF
+ dx = 2.0 ** -10
+ for x in range(90, 111):
+ est_pdf = (X.cdf(x + dx) - X.cdf(x)) / dx
+ self.assertAlmostEqual(X.pdf(x), est_pdf, places=4)
+ # Error case: variance is zero
+ Y = NormalDist(100, 0)
+ with self.assertRaises(statistics.StatisticsError):
+ Y.pdf(90)
+
+ def test_cdf(self):
+ NormalDist = statistics.NormalDist
+ X = NormalDist(100, 15)
+ cdfs = [X.cdf(x) for x in range(1, 200)]
+ self.assertEqual(set(map(type, cdfs)), {float})
+ # Verify montonic
+ self.assertEqual(cdfs, sorted(cdfs))
+ # Verify center
+ self.assertAlmostEqual(X.cdf(100), 0.50)
+ # Error case: variance is zero
+ Y = NormalDist(100, 0)
+ with self.assertRaises(statistics.StatisticsError):
+ Y.cdf(90)
+
+ def test_same_type_addition_and_subtraction(self):
+ NormalDist = statistics.NormalDist
+ X = NormalDist(100, 12)
+ Y = NormalDist(40, 5)
+ self.assertEqual(X + Y, NormalDist(140, 13)) # __add__
+ self.assertEqual(X - Y, NormalDist(60, 13)) # __sub__
+
+ def test_translation_and_scaling(self):
+ NormalDist = statistics.NormalDist
+ X = NormalDist(100, 15)
+ y = 10
+ self.assertEqual(+X, NormalDist(100, 15)) # __pos__
+ self.assertEqual(-X, NormalDist(-100, 15)) # __neg__
+ self.assertEqual(X + y, NormalDist(110, 15)) # __add__
+ self.assertEqual(y + X, NormalDist(110, 15)) # __radd__
+ self.assertEqual(X - y, NormalDist(90, 15)) # __sub__
+ self.assertEqual(y - X, NormalDist(-90, 15)) # __rsub__
+ self.assertEqual(X * y, NormalDist(1000, 150)) # __mul__
+ self.assertEqual(y * X, NormalDist(1000, 150)) # __rmul__
+ self.assertEqual(X / y, NormalDist(10, 1.5)) # __truediv__
+ with self.assertRaises(TypeError):
+ y / X
+
+ def test_equality(self):
+ NormalDist = statistics.NormalDist
+ nd1 = NormalDist()
+ nd2 = NormalDist(2, 4)
+ nd3 = NormalDist()
+ self.assertNotEqual(nd1, nd2)
+ self.assertEqual(nd1, nd3)
+
+ # Test NotImplemented when types are different
+ class A:
+ def __eq__(self, other):
+ return 10
+ a = A()
+ self.assertEqual(nd1.__eq__(a), NotImplemented)
+ self.assertEqual(nd1 == a, 10)
+ self.assertEqual(a == nd1, 10)
+
+ # All subclasses to compare equal giving the same behavior
+ # as list, tuple, int, float, complex, str, dict, set, etc.
+ class SizedNormalDist(NormalDist):
+ def __init__(self, mu, sigma, n):
+ super().__init__(mu, sigma)
+ self.n = n
+ s = SizedNormalDist(100, 15, 57)
+ nd4 = NormalDist(100, 15)
+ self.assertEqual(s, nd4)
+
+ # Don't allow duck type equality because we wouldn't
+ # want a lognormal distribution to compare equal
+ # to a normal distribution with the same parameters
+ class LognormalDist:
+ def __init__(self, mu, sigma):
+ self.mu = mu
+ self.sigma = sigma
+ lnd = LognormalDist(100, 15)
+ nd = NormalDist(100, 15)
+ self.assertNotEqual(nd, lnd)
+
+ def test_pickle_and_copy(self):
+ nd = statistics.NormalDist(37.5, 5.625)
+ nd1 = copy.copy(nd)
+ self.assertEqual(nd, nd1)
+ nd2 = copy.deepcopy(nd)
+ self.assertEqual(nd, nd2)
+ nd3 = pickle.loads(pickle.dumps(nd))
+ self.assertEqual(nd, nd3)
+
+ def test_repr(self):
+ nd = statistics.NormalDist(37.5, 5.625)
+ self.assertEqual(repr(nd), 'NormalDist(mu=37.5, sigma=5.625)')
+
# === Run tests ===
diff --git a/Misc/NEWS.d/next/Library/2019-02-21-15-47-00.bpo-36018.qt7QUe.rst b/Misc/NEWS.d/next/Library/2019-02-21-15-47-00.bpo-36018.qt7QUe.rst
new file mode 100644
index 000000000000..bba47f4ea91e
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-02-21-15-47-00.bpo-36018.qt7QUe.rst
@@ -0,0 +1,3 @@
+Add statistics.NormalDist, a tool for creating and manipulating normal
+distributions of random variable. Features a composite class that treats
+the mean and standard deviation of measurement data as single entity.
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