Exact critical values of Kolmogorov-Smirnov test for discrete random variables

The nonparametric Kolmogorov-Smirnov goodness of fit test is employed to test if a random sample comes from a specified continuous distribution function. When this hypothesis is not satisfied the test is no longer applicable accurately. In the last years relatively little attention has been paid to the problems of the application of Kolmogorov- Smirnov test for discrete distributions. In this paper we present a survey of the previous works, we propose a procedure to apply the test to discrete random variables and we define the corresponding statistic. Moreover for some given distributions the exact critical values are tabulated and a comparison with the continuous case is made.