Fix p-values workaround computation

Author: jaime-cespedes-sisniega

frouros/callbacks/batch/permutation_test.py

@@ -4,10 +4,9 @@
 from typing import Any, Callable, Dict, List, Optional, Tuple
 
 import numpy as np  # type: ignore
-from scipy.stats import norm  # type: ignore
 
 from frouros.callbacks.batch.base import BaseCallbackBatch
-from frouros.utils.stats import permutation, z_score
+from frouros.utils.stats import permutation
 
 
 class PermutationTestDistanceBased(BaseCallbackBatch):
@@ -122,13 +121,7 @@ def _calculate_p_value(  # pylint: disable=too-many-arguments
             verbose=verbose,
         )
         permuted_statistic = np.array(permuted_statistic)
-        # Use z-score to calculate p-value
-        observed_z_score = z_score(
-            value=observed_statistic,
-            mean=permuted_statistic.mean(),  # type: ignore
-            std=permuted_statistic.std(),  # type: ignore
-        )
-        p_value = norm.sf(np.abs(observed_z_score)) * 2
+        p_value = (permuted_statistic >= observed_statistic).mean()  # type: ignore
         return permuted_statistic, p_value
 
     def on_compare_end(self, **kwargs) -> None:

frouros/tests/integration/test_callback.py

@@ -54,13 +54,13 @@
     "detector_class, expected_distance, expected_p_value",
     [
         (BhattacharyyaDistance, 0.55516059, 0.0),
-        (EMD, 3.85346006, 9.21632493e-101),
-        (HellingerDistance, 0.74509099, 3.13808126e-50),
-        (HINormalizedComplement, 0.78, 1.31340683e-55),
-        (JS, 0.67010107, 2.30485343e-63),
-        (KL, np.inf, np.nan),
-        (MMD, 0.69509004, 2.53277069e-137),
-        (PSI, 461.20379435, 4.45088795e-238),
+        (EMD, 3.85346006, 0.0),
+        (HellingerDistance, 0.74509099, 0.0),
+        (HINormalizedComplement, 0.78, 0.0),
+        (JS, 0.67010107, 0.0),
+        (KL, np.inf, 0.06),
+        (MMD, 0.69509004, 0.0),
+        (PSI, 461.20379435, 0.0),
     ],
 )
 def test_batch_permutation_test_data_univariate_different_distribution(
@@ -103,7 +103,6 @@ def test_batch_permutation_test_data_univariate_different_distribution(
     assert np.isclose(
         callback_logs[permutation_test_name]["p_value"],
         expected_p_value,
-        equal_nan=True,
     )