Simplify and tighten the distribution test

Lib/test/test_statistics.py

@@ -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):