Accession Number : AD0681172

Title :   ON THE PROBABILITY THAT X < Y WHEN X AND Y ARE DEPENDENT,

Corporate Author : SYSTEM DEVELOPMENT CORP SANTA MONICA CALIF

Personal Author(s) : Murthy,Vrudhula K. ; Lientz,Bennet P.

Report Date : 21 JAN 1969

Pagination or Media Count : 17

Abstract : The paper is a generalization of earlier papers by Birnbaum and McCarty. Assuming that X and Y are independently distributed, Birnbaum and McCarty obtain distribution free upper confidence bounds for P(X<Y). In this paper, the Wilcoxon-Mann-Whitney Statistic for estimating p = P(X<Y) is generalized to the case where X and Y have an arbitrary joint bivariate distribution. The consistency and asymptotic normality of the statistics for estimating p are established based on a random sample (x sub i, y sub i), i = 1, 2, ... N of size N from the joint distribution F(x,y) of X and Y. A method of obtaining a distribution-free upper confidence bound for p is given. Some applications and extensions are discussed in the section on concluding remarks. (Author)

Descriptors :   (*CONFIDENCE LIMITS, DECISION THEORY), STATISTICAL DISTRIBUTIONS, PROBABILITY, SAMPLING, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE