Identifying All Distinct Sample P-P Plots, with an Application to the Exact Finite Sample Distribution of the L₁-FCvM Test Statistic

Abstract

P-p plots contain all the information that is needed for scale-invariant comparisons. Indeed, Empirical Distribution Function (EDF) tests translate sample p-p plots into a single number. In this paper we characterize the set of all distinct p-p plots for two balanced sample of size n absent ties. Distributions of EDF test statistics are embedded in this set. It is thus used to derive the exact finite sample distribution of the L₁-version of the Fisz-Cramér-von Mises test. Comparing this 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.

Keywords: Sample p-p plot, EDF test, finite sample distribution, limiting distribution

JEL Classification: C12, C14, C46