On the Exact Finite Sample Distribution of the L1 -FCvM Test Statistic

We derive the exact finite sample distribution of the <I>L<SUB>1</SUB></I>-version ofthe Fisz-Cramér-von Mises test statistic (<I>L<SUB>1</SUB></I>-FCvM). We first characterizethe set of all distinct sample p-p plots for two balanced sampleof size <I>n</I> absent ties. Next, we order this set according to the correspondingvalue of <I>L₁</I>-FCvM. Finally, we link these values to theprobabilities that the underlying p-p plots emerge. Comparing the finitesample distribution with the (known) limiting distribution showsthat the latter can always be used for hypothesis testing: although forfinite samples the critical percentiles of the limiting distribution differfrom the exact values, this will not lead to differences in the rejectionof the underlying hypothesis.