TESTS FOR EXPONENTIALITY AGAINST INCREASING FAILURE RATE AVERAGE ALTERNATIVES WITH CENSORED-DATA

The J(b) 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 K(b) (2) 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 F(T)BAR = FGBARBAR, where FBAR and GBAR are the survival functions associated with two independent competing risks. We decompose a statistic K(b) (1), a constant multiple of J(b), which tests for the exponentiality of T, into the sum of two statistics, K(b) (2) and K(b) (3), where K(b) (2) (K(b) (3)), test for the exponentiality of FBAR (GBAR), as above.