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Minor edit: Simplify and tighten the distribution test #118585

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May 5, 2024
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Minor edit: Simplify and tighten the distribution test #118585

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21 changes: 11 additions & 10 deletions Lib/test/test_statistics.py
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Original file line number Diff line number Diff line change
Expand Up @@ -2482,29 +2482,30 @@ def test_kde_random(self):
# Approximate distribution test: Compare a random sample to the expected distribution

data = [-2.1, -1.3, -0.4, 1.9, 5.1, 6.2, 7.8, 14.3, 15.1, 15.3, 15.8, 17.0]
xarr = [x / 10 for x in range(-100, 250)]
n = 1_000_000
h = 1.75
dx = 0.1

def p_expected(x):
return F_hat(x + dx) - F_hat(x - dx)

def p_observed(x):
# P(x-dx <= X < x+dx) / (2*dx)
i = bisect.bisect_left(big_sample, x - dx)
j = bisect.bisect_right(big_sample, x + dx)
# P(x <= X < x+dx)
i = bisect.bisect_left(big_sample, x)
j = bisect.bisect_left(big_sample, x + dx)
return (j - i) / len(big_sample)

def p_expected(x):
# P(x <= X < x+dx)
return F_hat(x + dx) - F_hat(x)

for kernel in kernels:
with self.subTest(kernel=kernel):

F_hat = statistics.kde(data, h, kernel, cumulative=True)
rand = kde_random(data, h, kernel, seed=8675309**2)
big_sample = sorted([rand() for i in range(n)])
F_hat = statistics.kde(data, h, kernel, cumulative=True)

for x in range(-40, 190):
x /= 10
self.assertTrue(math.isclose(p_observed(x), p_expected(x), abs_tol=0.001))
for x in xarr:
self.assertTrue(math.isclose(p_observed(x), p_expected(x), abs_tol=0.0005))


class TestQuantiles(unittest.TestCase):
Expand Down