New tests for exponentiality based on a characterization with random shift

Abstract

We derive the efficiencies of two new tests for exponentiality which are based on a recent characterization that uses the idea of a random shift. The finite-sample performance of the newly proposed tests is evaluated and compared to other existing tests by means of Monte Carlo simulations. It is found that the new tests perform favourably when compared to the other tests. Overall the best performing tests seem to be our new Kolmogorov-Smirnov type test, the score function based test by Cox and Oakes, and the Kolmogorov-Smirnov type test based on the mean residual life. The tests are also applied to a real-world data set with i.i.d. data as well as to simulated data from a Cox-proportional hazards model, where we test whether the so-called Cox-Snell residuals follow a standard exponential distribution