New class of supremum-type exponentiality tests based on V-empirical Laplace transforms and Puri-Rubin characterization

Abstract

We propose a new class of scale free goodness-of-fit tests for the exponential distribution based on the Puri-Rubin characterization. For the construction of test statistics we employ weighted L^\infty distance between V-empirical Laplace transforms of the random variables that appear in the characterization. We derive the asymptotic properties, and to assess the quality of the tests, we calculate the approximate Bahadur efficiency for some common close alternatives. 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.