bpo-36324: NormalDist() add more tests and update comments (GH-12476)
* Improve coverage.
* Note inherent limitations of the accuracy tests
https://bugs.python.org/issue36324
diff --git a/Lib/test/test_statistics.py b/Lib/test/test_statistics.py
index 02cbebd..485ffe2 100644
--- a/Lib/test/test_statistics.py
+++ b/Lib/test/test_statistics.py
@@ -2040,6 +2040,13 @@
class TestNormalDist(unittest.TestCase):
+ # General note on precision: The pdf(), cdf(), and overlap() methods
+ # depend on functions in the math libraries that do not make
+ # explicit accuracy guarantees. Accordingly, some of the accuracy
+ # tests below may fail if the underlying math functions are
+ # inaccurate. There isn't much we can do about this short of
+ # implementing our own implementations from scratch.
+
def test_slots(self):
nd = statistics.NormalDist(300, 23)
with self.assertRaises(TypeError):
@@ -2062,6 +2069,12 @@
with self.assertRaises(statistics.StatisticsError):
statistics.NormalDist(500, -10)
+ # verify that subclass type is honored
+ class NewNormalDist(statistics.NormalDist):
+ pass
+ nnd = NewNormalDist(200, 5)
+ self.assertEqual(type(nnd), NewNormalDist)
+
def test_alternative_constructor(self):
NormalDist = statistics.NormalDist
data = [96, 107, 90, 92, 110]
@@ -2077,6 +2090,12 @@
with self.assertRaises(statistics.StatisticsError):
NormalDist.from_samples([10]) # only one input
+ # verify that subclass type is honored
+ class NewNormalDist(NormalDist):
+ pass
+ nnd = NewNormalDist.from_samples(data)
+ self.assertEqual(type(nnd), NewNormalDist)
+
def test_sample_generation(self):
NormalDist = statistics.NormalDist
mu, sigma = 10_000, 3.0
@@ -2099,12 +2118,6 @@
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)
@@ -2151,8 +2164,8 @@
self.assertEqual(set(map(type, cdfs)), {float})
# Verify montonic
self.assertEqual(cdfs, sorted(cdfs))
- # Verify center
- self.assertAlmostEqual(X.cdf(100), 0.50)
+ # Verify center (should be exact)
+ self.assertEqual(X.cdf(100), 0.50)
# Check against a table of known values
# https://en.wikipedia.org/wiki/Standard_normal_table#Cumulative
Z = NormalDist()
@@ -2216,10 +2229,11 @@
p = 1.0 - p
self.assertAlmostEqual(iq.cdf(iq.inv_cdf(p)), p)
- # Now apply cdf() first. At six sigmas, the round-trip
- # loses a lot of precision, so only check to 6 places.
- for x in range(10, 190):
- self.assertAlmostEqual(iq.inv_cdf(iq.cdf(x)), x, places=6)
+ # Now apply cdf() first. Near the tails, the round-trip loses
+ # precision and is ill-conditioned (small changes in the inputs
+ # give large changes in the output), so only check to 5 places.
+ for x in range(200):
+ self.assertAlmostEqual(iq.inv_cdf(iq.cdf(x)), x, places=5)
# Error cases:
with self.assertRaises(statistics.StatisticsError):
@@ -2237,6 +2251,9 @@
iq.sigma = -0.1 # sigma under zero
iq.inv_cdf(0.5)
+ # Special values
+ self.assertTrue(math.isnan(Z.inv_cdf(float('NaN'))))
+
def test_overlap(self):
NormalDist = statistics.NormalDist
@@ -2275,6 +2292,7 @@
(NormalDist(-100, 15), NormalDist(110, 15)),
(NormalDist(-100, 15), NormalDist(-110, 15)),
# Misc cases with unequal standard deviations
+ (NormalDist(100, 12), NormalDist(100, 15)),
(NormalDist(100, 12), NormalDist(110, 15)),
(NormalDist(100, 12), NormalDist(150, 15)),
(NormalDist(100, 12), NormalDist(150, 35)),
@@ -2305,18 +2323,6 @@
self.assertEqual(X.stdev, 15)
self.assertEqual(X.variance, 225)
- def test_unary_operations(self):
- NormalDist = statistics.NormalDist
- X = NormalDist(100, 12)
- Y = +X
- self.assertIsNot(X, Y)
- self.assertEqual(X.mu, Y.mu)
- self.assertEqual(X.sigma, Y.sigma)
- Y = -X
- self.assertIsNot(X, Y)
- self.assertEqual(X.mu, -Y.mu)
- self.assertEqual(X.sigma, Y.sigma)
-
def test_same_type_addition_and_subtraction(self):
NormalDist = statistics.NormalDist
X = NormalDist(100, 12)
@@ -2340,13 +2346,27 @@
with self.assertRaises(TypeError): # __rtruediv__
y / X
+ def test_unary_operations(self):
+ NormalDist = statistics.NormalDist
+ X = NormalDist(100, 12)
+ Y = +X
+ self.assertIsNot(X, Y)
+ self.assertEqual(X.mu, Y.mu)
+ self.assertEqual(X.sigma, Y.sigma)
+ Y = -X
+ self.assertIsNot(X, Y)
+ self.assertEqual(X.mu, -Y.mu)
+ self.assertEqual(X.sigma, Y.sigma)
+
def test_equality(self):
NormalDist = statistics.NormalDist
nd1 = NormalDist()
nd2 = NormalDist(2, 4)
nd3 = NormalDist()
+ nd4 = NormalDist(2, 4)
self.assertNotEqual(nd1, nd2)
self.assertEqual(nd1, nd3)
+ self.assertEqual(nd2, nd4)
# Test NotImplemented when types are different
class A: