In this thesis, tail conditional expectation (TCE) in risk analysis, an important measure for right-tail risk, is presented. This value is generally based on the quantile of the loss distribution. Explicit formulas of several tail conditional expectations and inequality measures for Dagum-type models are derived. In addition, a new class of weighted Burr-III (WBIII) distribution is presented. The statistical properties of this distribution including hazard and reverse hazard functions, moments, coefficient of variation, skewness, and kurtosis, inequality measures, entropy are derived. Also, Fisher information and maximum likelihood estimates of the model parameters are obtained.
","abstract_html":"<p>In this thesis, tail conditional expectation (TCE) in risk analysis, an important measure for right-tail risk, is presented. This value is generally based on the quantile of the loss distribution. Explicit formulas of several tail conditional expectations and inequality measures for Dagum-type models are derived. In addition, a new class of weighted Burr-III (WBIII) distribution is presented. The statistical properties of this distribution including hazard and reverse hazard functions, moments, coefficient of variation, skewness, and kurtosis, inequality measures, entropy are derived. Also, Fisher information and maximum likelihood estimates of the model parameters are obtained.</p>","abstract_has_math":false,"creators":["AL Buqami, Meznah R"],"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":2013,"date_issued":"2013-01-01T08:00:00Z","date_published":"2013-01-01T08:00:00Z","updated_at":"2026-07-24T02:27:41Z","subjects":["ETD","income inequality","tail conditional expectation","weighted BurrIII distribution","risk measure","average loss","Physical Sciences and Mathematics","Statistical Methodology","Statistical Models","Statistics and Probability","Survival Analysis"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/880","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":["AL Buqami, Meznah R"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2018-12-10T08:00:00Z"]},{"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","income inequality","tail conditional expectation","weighted BurrIII distribution","risk measure","average loss","Physical Sciences and Mathematics","Statistical Methodology","Statistical Models","Statistics and Probability","Survival Analysis"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/880"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, tail conditional expectation (TCE) in risk analysis, an important measure for right-tail risk, is presented. This value is generally based on the quantile of the loss distribution. Explicit formulas of several tail conditional expectations and inequality measures for Dagum-type models are derived. In addition, a new class of weighted Burr-III (WBIII) distribution is presented. The statistical properties of this distribution including hazard and reverse hazard functions, moments, coefficient of variation, skewness, and kurtosis, inequality measures, entropy are derived. Also, Fisher information and maximum likelihood estimates of the model parameters are obtained.
"]},{"key":"dc:title","label":"Title","values":["Income Inequality Measures and Statistical Properties of Weighted Burr-type and Related Distributions"]}]}],"canonical_facts":{"dc:contributor":["Charles Champ","Hani Samawi"],"dc:creator":["AL Buqami, Meznah R"],"dc:date.available":["2018-12-10T08:00:00Z"],"dc:description.abstract":["In this thesis, tail conditional expectation (TCE) in risk analysis, an important measure for right-tail risk, is presented. This value is generally based on the quantile of the loss distribution. Explicit formulas of several tail conditional expectations and inequality measures for Dagum-type models are derived. In addition, a new class of weighted Burr-III (WBIII) distribution is presented. The statistical properties of this distribution including hazard and reverse hazard functions, moments, coefficient of variation, skewness, and kurtosis, inequality measures, entropy are derived. Also, Fisher information and maximum likelihood estimates of the model parameters are obtained.
"],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/880"],"dc:subject":["ETD","income inequality","tail conditional expectation","weighted BurrIII distribution","risk measure","average loss","Physical Sciences and Mathematics","Statistical Methodology","Statistical Models","Statistics and Probability","Survival Analysis"],"dc:title":["Income Inequality Measures and Statistical Properties of Weighted Burr-type and Related Distributions"],"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":"2026-07-24T02:27:41Z"}