The exact null distribution of the generalized Hollander–Proschan type test for NBUE alternatives

In this note we derive the exact null distribution for the test statistic γj∗(Fn) proposed by Anis and Mitra (2011) for testing exponentiality against NBUE alternatives. As a special case, we obtain the exact null distribution for the test statistic K∗K∗ proposed by Hollander and Proschan (1975). Selected critical values for different sizes are tabulated for these two statistics. Some remarks concerning the benefits of using the exact distribution are made.