An alternative to the Kolmogrov-Smirnov two-sample test

An alternative to the Kolmogorov-Smirnov two-sample test based on the test statistic is suggested, where #{} denotes the cardinality of the set. For the null-hypothesis case the probability distribution and its low-order moments are derived in the exact and in an approximateversion. Based on Monte Carlo estimates the power of the two tests are compared for samples of uniform, normal, and gamma distributions Pure shifts of expectation and variance of one of the sample distributions are considered as well as the case of shifts in both parameters; other situations considered concern samples from different distributions and samples from disturbed distributions. The results indicate that the test based on T is more powerful than the Kolmogorov-Smirnov test for samples of the uniform distribution which differ in the expectation and in the case of disturbed distributions.