Further moments inequalities of life distributions with hypothesis testing applications: the IFRA, NBUC and DMRL classes

Abstract

In a recent article, Ahmad (J. Statist. Plann. Inference 92 (2001) 121–132), one of the authors presented moments inequalities for classes of life distributions including increasing failure rate, new better than used, new better than used in expectation and harmonic new better than used in expectation. He then uses these inequalities to devise new testing procedures for exponentiality against an alternative among the four classes indicated above. Three other classes, the increasing failure rate average, the new is better than used in convex ordering and the decreasing mean residual lifetime, were left untreated since the techniques employed in Ahmad (2001) did not apply to them. Thus, new techniques are developed here to address these three classes completing the study of the perennial group of life distributions. The tests proposed here are simpler than those known in the literature with very good efficiencies.