Kolmogorov-Smirnov Test for Discrete Distributions

The Kolmogorov-Smirnov goodness-of-fit test is exact only when the hypothesized distribution is continuous, but recently Conover has extended the Kolmogorov-Smirnov test to obtain a test that is exact in the case of discrete distributions. Reasons for using this procedure instead of the regular Kolmogorov-Smirnov test when the hypothesized distribution is discrete are given. A computer subroutine is developed to allow easy use of the procedure. The subroutine is then used to demonstrate the conservatism of the regular Kolmogorov-Smirnov test in this case and to investigate some properties of the asymptotic distributions of the test statistics.