Computer Security and Cryptography

5.2 THE KOLMOGOROV – SMIRNOV TEST

Figure 5.1 plots the sample distribution function for n = 100 and n = 1000 samples of data derived from a uniform distribution function F(x). The Kolmogorov – Smirnov Test is a goodness-of-fit test; is a sample of n data values X₀, X₁,…, X_n−1, derived from independent and identical random trials consistent with a specified distribution function F(x) = Pr{X_j ≤ x}? The law of large numbers implies that the sample distribution function

Figure 5.1 Sample Distribution Function (a) n = 100; (b) n = 1000.

converges as the sample size n increases

with probability 1.

The Kolmogorov–Smirnov statistics

measures the vertical deviation of F(x) from the sample distribution function , where

• measures the deviation when and
• the deviation when

The Kolmogorov – Smirnov ...