Exponentiality tests based on Basu characterization

Abstract

This paper proposes and studies two new classes of tests for exponentiality. Both of them are based on Basu's characterization of the exponential distribution. The null distributions of the test statistics are parameter free. Moreover, conveniently normalized, they are asymptotically normally distributed. The large sample behaviour of the proposed tests is studied for fixed alternatives, and for local alternatives by means of the approximate local Bahadur efficiency. The finite sample performance of the new tests is studied via simulation. Two of the new tests present a very high relative local Bahadur efficiency and a competing behaviour against fixed alternatives in relation to existing tests.