Accession Number : AD0711806

Title :   ISOTONIC TESTS FOR CONVEX ORDERINGS,

Corporate Author : CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER

Personal Author(s) : Barlow,Richard E.

Report Date : JUL 1970

Pagination or Media Count : 49

Abstract : Assume F and G are distributions on (0, infinity) with densities f and g , respectively. If G sup-1F is convex on the support of F (an interval), then r(x) = d/dx G sup-1 F(x) = f(x)/g(G sup-1 F(x)) (the generalized failure rate function) is nondecreasing in x epsilon (0, infinity) . We assume G known, r nondecreasing and consider the problem of testing r constant versus r nondecreasing and not constant. A test based on the cumulative total time on test statistic is proposed and studied for this problem. It is shown for the cases G(x) = x , x > or = 0 and G(x) - 1 --e sup-x , x > or = 0 that this test is asymptotically minimax over a class of alternatives based on the Kolmogorov distance and with respect to a class of generalized scores tests. (Author)

Descriptors :   (*STATISTICAL TESTS, CONVEX SETS), MINIMAX TECHNIQUE, DISTRIBUTION FUNCTIONS, ASYMPTOTIC SERIES

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE