Kolmogorov–Smirnov Test

Definition

The Kolmogorov–Smirnov test (KS test) is a non-parametric test for the equality of continuous, distribution functions.

The Kolmogorov–Smirnov test statistic for a given CDF $F$ is defined as $KS={\sup }_t|F_n(t)-F(t)|={\max }_{1\le i\le n}\left[\frac{1}{n}-F(t_i),F(t_i)-\frac{i-1}{n}\right]$ where $F_n$ is the Empirical Distribution Function based on the i.i.d. random variables $X_i,i=1,2,\dots ,n$.