Create ks_test.py

Author: dple

ks_test.py

@@ -0,0 +1,45 @@
+"""
+Implement Kolmogorov–Smirnov test that can be used to compare two non-parametric variables
+https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test
+
+Phong D. Le  -  le.duc.phong@gmail.com
+"""
+
+import numpy as np
+from scipy.stats import iqr, tstd
+def KSTest(X, Y):
+    """
+    Calculate Kolmogorov–Smirnov statistic of two samples
+
+    Formula:  D = max(abs(CDF(X) - CDF(Y)))
+    """
+    # Calculate the number of bins using Sturges' rule
+    # Formula:    bins = ceil(1 + log2(n))
+    bins1 = np.ceil(1 + np.log2(len(X))).astype('int')
+    bins2 = np.ceil(1 + np.log2(len(Y))).astype('int')
+    # Number of bins will be the average of two bins
+    bins = np.ceil((bins1 + bins2)/2).astype('int')
+
+    # Split data of two variables in the same range and the same number of bins
+    amax = max(np.max(X), np.max(Y))
+    amin = min(np.min(X), np.min(Y))
+    histX, _ = np.histogram(X, bins=bins, range=[amin, amax])
+    histY, _ = np.histogram(Y, bins=bins, range=[amin, amax])
+    # Get the probability of bins
+    px = histX / histX.sum()
+    py = histY / histY.sum()
+    # Get cumulative distribution probability
+    cdfX = np.cumsum(px)
+    cdfY = np.cumsum(py)
+
+    return max(abs(cdfX - cdfY))
+
+
+if __name__ == '__main__':
+    # X, a random Gaussian distribution
+    X = np.random.normal(0, 100, 1000)
+    # Y, a random bivariate Gaussian distribution
+    Y = np.concatenate([np.random.normal(0, 50, 500),
+                        np.random.normal(200, 70, 500)])
+
+    print('Kolmogorov–Smirnov test: D(X,Y) = {}'.format(KSTest(X, Y)))