Make the validation condition for random distributions lenient (#550)

* Make the validation condition for random distributions lenient

* Fix typo

* Catch too small standard variations against theoretical values as well

* Replace unnecessary NumPy calls with Python primitives

* Tighten the tolerance

tests/integration/utils/random.py

@@ -143,7 +143,9 @@ def zipf(self, alpha, shape, dtype):
         return num.random.zipf(alpha, shape, dtype)
 
 
-def assert_distribution(a, theo_mean, theo_stdev, tolerance=1e-2):
+def assert_distribution(
+    a, theo_mean, theo_stdev, mean_tol=1e-2, stdev_tol=1.0
+):
     if True:
         aa = np.array(a)
         average = np.mean(aa)
@@ -154,12 +156,16 @@ def assert_distribution(a, theo_mean, theo_stdev, tolerance=1e-2):
             num.mean((a - average) ** 2)
         )  # num.std(a) -> does not work
     print(
-        f"average = {average} - expected {theo_mean}"
-        + f", stdev = {stdev} - expected {theo_stdev}\n"
-    )
-    assert np.abs(theo_mean - average) < tolerance * np.max(
-        (1.0, np.abs(theo_mean))
-    )
-    assert np.abs(theo_stdev - stdev) < tolerance * np.max(
-        (1.0, np.abs(theo_stdev))
+        f"average = {average} - theoretical {theo_mean}"
+        + f", stdev = {stdev} - theoretical {theo_stdev}\n"
     )
+    assert abs(theo_mean - average) < mean_tol * max(1.0, abs(theo_mean))
+    # the theoretical standard deviation can't be 0
+    assert theo_stdev != 0
+    # TODO: this check is not a good proxy to validating that the samples
+    #       respect the assumed random distribution unless we draw
+    #       extremely many samples. until we find a better validation
+    #       method, we make the check lenient to avoid random
+    #       failures in the CI. (we still need the check to catch
+    #       the cases that are obviously wrong.)
+    assert abs(theo_stdev - stdev) / min(theo_stdev, stdev) <= stdev_tol