L²-type exponentiality tests based on V-empirical Laplace transform and Puri-Rubin characterization

Abstract

In this paper we propose new goodness-of-fit tests that employ the equidistribution characterization of the exponential distribution due to Puri and Rubin. Based on V-empirical Laplace transforms of equidistributed statistics, test statistics of L²-type are constructed. They are degenerate V-statistics with estimated parameters. Their asymptotic properties are derived. To assess their quality, the approximate Bahadur efficiency is used. For small sample sizes, a simulated power study is performed. The tests are shown to be very efficient and powerful in comparison to many other exponentiality tests.