From 18ee50d5dad81124c3fa0121c1ed7be0cd21d3b2 Mon Sep 17 00:00:00 2001
From: Raymond Hettinger <rhettinger@users.noreply.github.com>
Date: Wed, 6 Mar 2019 02:31:14 -0800
Subject: [PATCH] Add more tests for pdf() and cdf() (GH-12190)

---
 Lib/test/test_statistics.py | 32 +++++++++++++++++++++++++++++---
 1 file changed, 29 insertions(+), 3 deletions(-)

diff --git a/Lib/test/test_statistics.py b/Lib/test/test_statistics.py
index 4adc5e4cbf4..3f14e63c23f 100644
--- a/Lib/test/test_statistics.py
+++ b/Lib/test/test_statistics.py
@@ -2101,14 +2101,28 @@ class TestNormalDist(unittest.TestCase):
         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))
+        for i in range(50):
+            self.assertAlmostEqual(X.pdf(100 - i), X.pdf(100 + i))
         # 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)
+        # Test vs table of known values -- CRC 26th Edition
+        Z = NormalDist()
+        for x, px in enumerate([
+            0.3989, 0.3989, 0.3989, 0.3988, 0.3986,
+            0.3984, 0.3982, 0.3980, 0.3977, 0.3973,
+            0.3970, 0.3965, 0.3961, 0.3956, 0.3951,
+            0.3945, 0.3939, 0.3932, 0.3925, 0.3918,
+            0.3910, 0.3902, 0.3894, 0.3885, 0.3876,
+            0.3867, 0.3857, 0.3847, 0.3836, 0.3825,
+            0.3814, 0.3802, 0.3790, 0.3778, 0.3765,
+            0.3752, 0.3739, 0.3725, 0.3712, 0.3697,
+            0.3683, 0.3668, 0.3653, 0.3637, 0.3621,
+            0.3605, 0.3589, 0.3572, 0.3555, 0.3538,
+        ]):
+            self.assertAlmostEqual(Z.pdf(x / 100.0), px, places=4)
         # Error case: variance is zero
         Y = NormalDist(100, 0)
         with self.assertRaises(statistics.StatisticsError):
@@ -2127,6 +2141,18 @@ class TestNormalDist(unittest.TestCase):
         self.assertEqual(cdfs, sorted(cdfs))
         # Verify center
         self.assertAlmostEqual(X.cdf(100), 0.50)
+        # Check against a table of known values
+        # https://en.wikipedia.org/wiki/Standard_normal_table#Cumulative
+        Z = NormalDist()
+        for z, cum_prob in [
+            (0.00, 0.50000), (0.01, 0.50399), (0.02, 0.50798),
+            (0.14, 0.55567), (0.29, 0.61409), (0.33, 0.62930),
+            (0.54, 0.70540), (0.60, 0.72575), (1.17, 0.87900),
+            (1.60, 0.94520), (2.05, 0.97982), (2.89, 0.99807),
+            (3.52, 0.99978), (3.98, 0.99997), (4.07, 0.99998),
+            ]:
+            self.assertAlmostEqual(Z.cdf(z), cum_prob, places=5)
+            self.assertAlmostEqual(Z.cdf(-z), 1.0 - cum_prob, places=5)
         # Error case: variance is zero
         Y = NormalDist(100, 0)
         with self.assertRaises(statistics.StatisticsError):