ON THE PROBABILITY THAT X < Y WHEN X AND Y ARE DEPENDENT,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 21, 1969
- Accession Number
- AD0681172
Entities
People
- Bennet P. Lientz
- Vrudhula K. Murthy
Organizations
- System Development Corporation