Convex combination of two U-statistics for testing new better than used

Abstract

Testing exponentiality against positive ageing has been an active research area during the past three decades. A particular type of positive ageing, namely the new better than used distributions (NBU), is useful in studying replacement policies. Two classes of test statistic for testing exponentiality, both convex combinations of U-statistics, are proposed against the NBU alternative. The asymptotic distributions of the proposed classes are studied. Performance of members of the test classes is studied in terms of Pitman asymptotic relative efficiency in comparison with the tests due to Hollander and Proschan [6], and due to Ahmad [2]. It is observed that the proposed tests are better for certain values of the sub sample size and mixing coefficient.