Term of Award

Spring 2010

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Department

Department of Mathematical Sciences

Committee Chair

Broderick O. Oluyede

Committee Member 1

Charles Champ

Committee Member 2

Hani Samawi

Abstract

Strategies for the analysis of discrete data under order restrictions are discussed. We consider inference for sequences of binomial populations, and the corresponding risk difference, relative risk and odds ratios. These concepts are extended to deal with independent multinomial populations. Natural orderings such as stochastic ordering and cumulative ratio probability ordering are discussed. Methods are developed for the estimation and testing of differences between binomial as well as multinomial populations under order restrictions. In particular, inference for sequences of ordered binomial probabilities and cumulative probability ratios in multinomial populations are presented. Closed-form estimates of the multinomial parameters under order restrictions and test procedures for testing equality of two multinomial populations against the notion of cumulative probability ratio ordering which is stronger than stochastic ordering of the distributions are presented. Numerical examples are given to illustrate the techniques developed.

Included in

Mathematics Commons

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