A class of efficient tests for increasing-failure-rate-average distribution under random censoring

摘要

A class of tests for the increasing failure rate average (IFRA) alternatives under random censoring is proposed. The tests are based on a function of the Kaplan-Meier estimator. Most of the IFRA tests in the literature depend on the (nuisance) parameter that appears in the definition of IFRA, and the choice of this parameter is crucial in performing the tests. The proposed class of tests does not have this disadvantage. Under some regularity conditions, the asymptotic normality of the tests is established and asymptotically distribution-free tests are obtained by using estimators for the null standard deviations. The efficacies of the tests under the proportional hazard censoring model are studied. The proposed test is most efficient for the Weibull family of IFRA alternatives among the existing tests available for the censored data. The test is applied to published appliance data.