A diathered k-s staticstic

The Kolmogorov-Sruimov test depends for its distribution-free property on the observation that, if F() is the CDF of continuous random variable A then random variable F(X) is uniform on the interval [0,1]. That observation is false if F() is not continuous, a restriction on the applicability of the KS test. This paper introduces a generalization of the KS statistic that works for all distributions, including discrete ones.