Some consistent exponentiality tests based on Puri-Rubin and Desu characterizations

Abstract

We present new goodness-of-fit tests based on equidistribution type characterizations. For the construction of the test statistics, we employ L²-distance between the corresponding V-empirical distribution functions. The resulting test statistics are V-statistics, free of the scale parameter. The quality of tests is accessed through local Bahadur efficiencies, in case of large sample sizes, as well as empirical powers, for small and moderate sample sizes. In both criteria, our tests perform better for many common alternatives than the integral and supremum type tests based on the same characterizations.