On the Exact Finite Sample Distribution of the L-1-FCvM Test Statistic

Abstract

We derive the exact finite sample distribution of the L-1 -version of the Fisz-Cramer-von Mises test statistic (FCvM(1)). We first characterize the set of all distinct sample p-p plots for two balanced samples of size n absent ties. Next, we order this set according to the corresponding value of FCvM(1). Finally, we link these values to the probabilities that the underlying p-p plots emerge. Comparing the finite sample distribution with the (known) limiting distribution shows that the latter can always be used for hypothesis testing: although for finite samples the critical percentiles of the limiting distribution differ from the exact values, this will not lead to differences in the rejection of the underlying hypothesis.