In this thesis, new classes of distributions namely: exponentiated Kumaraswamy-Dagum (EKD), Log-exponentiated Kumaraswamy-Dagum (Log-EKD), McDonald Log-logistic (McLLog) and Gamma-Dagum (GD) distributions are presented. A thorough and comprehensive investigation of these classes of distributions is conducted. Mathematical properties of these classes of distributions including series expansion, hazard and reverse hazard functions, moments, generating functions, mean and median deviations, Bonferroni and Lorenz curves, distribution of order statistics, moments of order statistics and entropies are presented. Estimation of parameters of these distributions via maximum likelihood technique, Fisher information and asymptotic confidence intervals are given. Maximum likelihood estimation of the parameters of the exponentiated Kumaraswamy-Dagum distribution for censored data is constructed. Real data examples are presented to illustrate the usefulness and applicability of these proposed classes of distributions.
","abstract_html":"<p>In this thesis, new classes of distributions namely: exponentiated Kumaraswamy-Dagum (EKD), Log-exponentiated Kumaraswamy-Dagum (Log-EKD), McDonald Log-logistic (McLLog) and Gamma-Dagum (GD) distributions are presented. A thorough and comprehensive investigation of these classes of distributions is conducted. Mathematical properties of these classes of distributions including series expansion, hazard and reverse hazard functions, moments, generating functions, mean and median deviations, Bonferroni and Lorenz curves, distribution of order statistics, moments of order statistics and entropies are presented. Estimation of parameters of these distributions via maximum likelihood technique, Fisher information and asymptotic confidence intervals are given. Maximum likelihood estimation of the parameters of the exponentiated Kumaraswamy-Dagum distribution for censored data is constructed. Real data examples are presented to illustrate the usefulness and applicability of these proposed classes of distributions.</p>","abstract_has_math":false,"creators":["Huang, Shujiao"],"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","Arpita Chatterjee"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-01-01T08:00:00Z","date_published":"2014-01-01T08:00:00Z","updated_at":"2026-07-24T02:27:52Z","subjects":["ETD","Kumaraswamy Distribution; Dagum Distribution; McDonald Distribution; Log-logistic Distribution; Gamma Distribution","Applied Statistics","Probability"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/1158","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Charles Champ","Arpita Chatterjee"]},{"key":"dc:creator","label":"Author","values":["Huang, Shujiao"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2019-06-22T07:00:00Z"]},{"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","Kumaraswamy Distribution; Dagum Distribution; McDonald Distribution; Log-logistic Distribution; Gamma Distribution","Applied Statistics","Probability"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/1158"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, new classes of distributions namely: exponentiated Kumaraswamy-Dagum (EKD), Log-exponentiated Kumaraswamy-Dagum (Log-EKD), McDonald Log-logistic (McLLog) and Gamma-Dagum (GD) distributions are presented. A thorough and comprehensive investigation of these classes of distributions is conducted. Mathematical properties of these classes of distributions including series expansion, hazard and reverse hazard functions, moments, generating functions, mean and median deviations, Bonferroni and Lorenz curves, distribution of order statistics, moments of order statistics and entropies are presented. Estimation of parameters of these distributions via maximum likelihood technique, Fisher information and asymptotic confidence intervals are given. Maximum likelihood estimation of the parameters of the exponentiated Kumaraswamy-Dagum distribution for censored data is constructed. Real data examples are presented to illustrate the usefulness and applicability of these proposed classes of distributions.
"]},{"key":"dc:title","label":"Title","values":["Generalized Classes of Distributions with Applications to Income and Lifetime Data"]}]}],"canonical_facts":{"dc:contributor":["Charles Champ","Arpita Chatterjee"],"dc:creator":["Huang, Shujiao"],"dc:date.available":["2019-06-22T07:00:00Z"],"dc:description.abstract":["In this thesis, new classes of distributions namely: exponentiated Kumaraswamy-Dagum (EKD), Log-exponentiated Kumaraswamy-Dagum (Log-EKD), McDonald Log-logistic (McLLog) and Gamma-Dagum (GD) distributions are presented. A thorough and comprehensive investigation of these classes of distributions is conducted. Mathematical properties of these classes of distributions including series expansion, hazard and reverse hazard functions, moments, generating functions, mean and median deviations, Bonferroni and Lorenz curves, distribution of order statistics, moments of order statistics and entropies are presented. Estimation of parameters of these distributions via maximum likelihood technique, Fisher information and asymptotic confidence intervals are given. Maximum likelihood estimation of the parameters of the exponentiated Kumaraswamy-Dagum distribution for censored data is constructed. Real data examples are presented to illustrate the usefulness and applicability of these proposed classes of distributions.
"],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/1158"],"dc:subject":["ETD","Kumaraswamy Distribution; Dagum Distribution; McDonald Distribution; Log-logistic Distribution; Gamma Distribution","Applied Statistics","Probability"],"dc:title":["Generalized Classes of Distributions with Applications to Income and Lifetime Data"],"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":"2026-07-24T02:27:52Z"}