bpo-36018: Add the NormalDist class to the statistics module (GH-11973)

2 files changed, 332 insertions, 1 deletions

diff --git a/Lib/statistics.py b/Lib/statistics.py
index 8ecb906..a73001a 100644
--- a/Lib/statistics.py
+++ b/Lib/statistics.py
@@ -76,7 +76,7 @@ A single exception is defined: StatisticsError is a subclass of ValueError.
 
 """
 
-__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 @@ __all__ = [ 'StatisticsError',
 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 e351446..a65fbe8 100644
--- a/Lib/test/test_statistics.py
+++ b/Lib/test/test_statistics.py
@@ -5,9 +5,11 @@ approx_equal function.
 
 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 @@ class TestStdev(VarianceStdevMixin, NumericTestCase):
         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 ===