Inference for the K-sample problem based on precedence probabilities

Abstract

Rank based inference using independent random samples to compare K>1 continuous distributions, called the K-sample problem, based on precedence probabilities is developed and explored. There are many parametric and nonparametric approaches, most dealing with hypothesis testing, to this important, classical problem. Most existing tests are designed to detect differences among the location parameters of different distributions. Best known and most widely used of these is the F- test, which assumes normality. A comparable nonparametric test was developed by Kruskal and Wallis (1952). When dealing with location-scale families of distributions, both of these tests can perform poorly if the differences among the distributions are among their scale parameters and not in their location parameters. Overall, existing tests are not effective in detecting changes in both location and scale. In this dissertation, I propose a new class of rank-based, asymptotically distribution- free tests that are effective in detecting changes in both location and scale based on precedence probabilities. Let X_{i} be a random variable with distribution function F_{i} ; Also, let pi be the set of all permutations of the numbers (1,2,...,K) . Then P(X_{i_{1}}<...