Analysis of Discrete Data under Order Restrictions

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.

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (open access)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2010

Author dc:creator

• Campbell, Jeff

Contributors dc:contributor

• Charles Champ
• Hani Samawi

• ETD
• Binomial distributions
• Restricted estimates
• Multinomial distribution
• Test procedures
• Discrete groups
• Multivariate analysis
• Mathematics

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/653

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-1653