Testing Exponentiality Against NBUL Alternatives Using Positive and Negative Fractional Moments

In this note a moment inequality for the New is Better than Used in Laplace ordering (NBUL) class of lifetime distributions is derived. A simple test statistic for testing exponentiality against NBUL alternatives is constructed. The test statistic is proved to be asymptotically normal and consistent. Critical values obtained by a Monte Carlo simulation are tabulated for different sample sizes. The asymptotic relative efficiency of the test is also studied.