A class of goodness-of-fit tests based on a new characterization of the exponential distribution

Abstract

A new characterisation of the exponential distribution in the class of new better than used in expectation (NBUE) life distributions is presented. Utilising this characterisation, a new class of goodness-of-fit tests for exponentiality against NBUE alternatives is proposed. The tests are shown to be consistent, and the limiting distributions of the test statistics under the null and alternative hypotheses are derived. The newly proposed tests are compared to existing goodness-of-fit tests by means of Pitman and approximate Bahadur relative efficiencies. A limited Monte Carlo study is conducted to compare the various tests with regard to power for small and moderate sample sizes against a range of alternative distributions. Three members of the class of test statistics are identified as being at least as effective as established tests for exponentiality against NBUE alternatives.