Tests for exponentiality against increasing failure rate average alternatives with censored data

Abstract

The Jb, statistic of Deshpande (1983) for testing the exponentiality of the lifetime survival function [Fbar] against the increasing failure rate average class of non-exponential distributions is extended to a statistic which is appropriate for right censored data. It is assumed that the censoring variable with survival function [Gbar] is independent of the lifetime and that [Gbar] satisfies mild regularity conditions. We recast the above work in the competing risks framework. In that setup, the survival function of the lifetime variable T is [Fbar]T = [Fbar][Gbar], where [Fbar] and [Gbar] are the survival functions associated with two independent competing risks. We decompose a statistic , a constant multiple of Jb, which tests for the exponentiality of T, into the sum of two statistics, , where , test for the exponentiality of [Fbar]([Gbar]), as above.