{"id":{"repo_id":"gsu","oai_identifier":"oai:digitalcommons.georgiasouthern.edu:etd-1653"},"canonical_url":"https://search.dev.ndltd.org/etd/gsu/oai:digitalcommons.georgiasouthern.edu:etd-1653","repository":{"repo_id":"gsu","name":"Georgia Southern University","base_url":"https://digitalcommons.georgiasouthern.edu/do/oai/"},"display":{"title":"Analysis of Discrete Data under Order Restrictions","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Campbell, Jeff"],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (open access)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Charles Champ","Hani Samawi"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-05-01T07:00:00Z","date_published":"2010-05-01T07:00:00Z","updated_at":"2026-07-24T02:27:19Z","subjects":["ETD","Binomial distributions","Restricted estimates","Multinomial distribution","Test procedures","Discrete groups","Multivariate analysis","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/653","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Charles Champ","Hani Samawi"]},{"key":"dc:creator","label":"Author","values":["Campbell, Jeff"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2013-10-17T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis (open access)"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics (M.S.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ETD","Binomial distributions","Restricted estimates","Multinomial distribution","Test procedures","Discrete groups","Multivariate analysis","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/653"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Analysis of Discrete Data under Order Restrictions"]}]}],"canonical_facts":{"dc:contributor":["Charles Champ","Hani Samawi"],"dc:creator":["Campbell, Jeff"],"dc:date.available":["2013-10-17T07:00:00Z"],"dc:description.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."],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/653"],"dc:subject":["ETD","Binomial distributions","Restricted estimates","Multinomial distribution","Test procedures","Discrete groups","Multivariate analysis","Mathematics"],"dc:title":["Analysis of Discrete Data under Order Restrictions"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (open access)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:27:19Z"}