Invariance properties of some classical tests for exponentiality

We examine some classical tests for the exponentiality of independent, identically distributed data. We show that a large number of these tests have the same distribution if the data follow certain multivariate Liouville distributions. These results highlight the role that the assumption of independence plays in the behavior of the classical test statistics. We use these results to derive some characterizations of the exponential distributions among the Liouville distributions. (C) 1997 Elsevier Science B.V.