A class of tests for exponentiality against increasing failure rate average alternatives

Abstract

A class of tests is proposed for testing exponentiality against the increasing failure rate average class of nonexponential probability distributions. Some of these tests are consistent as well for the larger class, new better than used. Compared to its competitors these statistics are remarkably simple. They are U-statistics and hence asymptotically normally distributed. The asymptotic relative efficiency with respect to the Hollander-Proschan statistic and the cumulative total time on test statistic are reasonably high.