TESTS FOR MONOTONE FAILURE RATE BASED ON NORMALIZED SPACINGS
CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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Let X sub 1 ... X sub n be the order statistics of a random sample from a population with density f and distribution function F such that F0 0. Let qt ft1 - Ft be the failure rate of F. In testing H sub o qt lambda vs. H sub l qt vertical arrow, Proschan and Pyke Vth Berk. Symp. considered certain statistics based on R sub l, ..., R sub n, the ranks of the normalized sample spacings D sub i n - i l X sub i - X sub i-l, 1 or i or n, X sub o 0. They show that these statistics are asymptotically normal for fixed F and compute the efficacy of one of these statistics for selected distributions. This report shows that asymptotic normality holds also for sequences of alternatives approaching H sub o as n approaches infinity and conclude that the above efficacies yield Pitman efficiencies.
- Statistics and Probability