  In this note we derive the exact null distribution for the test statistic
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 proposed by Hollander and Proschan (1975). Selected critical
values for different size are tabulated for these two statistics. Some remarks
concerning the benefits of using the exact distribution are made.
