A Procedure to Find Exact Critical Values ofKolmogorov-Smirnov Test

The compatibility of a random sample of data with a given distribution can be checked with a goodness of fit test. Kolmogorov (1933) and Smirnov (1939 A) proposed the D n statistic based on the comparison between the hypothesized distribution function F (x) and the empirical distribution function of the sample S n (x): D n = sup -∞<x<∞ |S n (x)- F 0 (x)|. If F 0 (x) is continuous and under the null hypothesis, the distribution of D n is independent of F 0 (x), i.e. the test is distribution-free. In this paper we introduced a procedure providing the exact critical values of the Kolmogorov-Smirnov test for fixed significance levels. These values are obtained by a modification of the procedure proposed by Feller (1948). In particular, the distribution function of the test statistic is obtained by the solution of a linear system of equations whose coefficients are proper marginal and conditional probabilities. Moreover, a Matlab program provides the computation of the cumulative distribution function's value of D n statistic P(D n < D) for given values of n and D.