Some results on tests for Poisson processes

Abstract

It is shown that a test proposed by Barnard for Poisson processes, using certain distribution-free statistics, is not consistent against renewal alternatives. However, empirical evidence is given which suggests that a modification of this test due to Durbin results in relatively powerful tests of the Poisson hypothesis. A simple test based on Durbin's modification is described, and its asymptotic relative efficiency with respect to the asymptotically most powerful test against the alternative of a renewal process with gamma-distributed intervals is given.