Accession Number:

AD0711806

Title:

ISOTONIC TESTS FOR CONVEX ORDERINGS,

Descriptive Note:

Corporate Author:

CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER

Personal Author(s):

• Barlow,Richard E.

Report Date:

1970-07-01

Pagination or Media Count:

49.0

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 rx ddx G sup-1 Fx fxgG sup-1 Fx 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 Gx x , x or 0 and Gx - 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