Weibull distribution and its extended families has been widely studied in lifetime applications. Based on the Weibull-G family of distributions and the exponentiated Weibull distribution, we study in detail two new classes of distributions, namely, Gamma-Weibull-G family of distributions (GWG) and gamma-exponentiated or generalized modified Weibull (GEMW) distribution. Some special models in these new classes are discussed. Statistical properties of these family of distributions, such as expansion of density function, hazard and reverse hazard functions, quantile function, moments, incomplete moments, generating functions, mean deviations, Bonferroni and Lorenz curves and order statistics are presented. For the GEMW, we also present Renyi entropy, estimation of parameters by using method of maximum likelihood, asymptotic confidence intervals and applications using real data.
","abstract_html":"<p>Weibull distribution and its extended families has been widely studied in lifetime applications. Based on the Weibull-G family of distributions and the exponentiated Weibull distribution, we study in detail two new classes of distributions, namely, Gamma-Weibull-G family of distributions (GWG) and gamma-exponentiated or generalized modified Weibull (GEMW) distribution. Some special models in these new classes are discussed. Statistical properties of these family of distributions, such as expansion of density function, hazard and reverse hazard functions, quantile function, moments, incomplete moments, generating functions, mean deviations, Bonferroni and Lorenz curves and order statistics are presented. For the GEMW, we also present Renyi entropy, estimation of parameters by using method of maximum likelihood, asymptotic confidence intervals and applications using real data.</p>","abstract_has_math":false,"creators":["Pu, Shusen"],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (restricted to Georgia Southern)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Charles Champ","Daniel Linder"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-01-01T08:00:00Z","date_published":"2014-01-01T08:00:00Z","updated_at":"2026-07-24T02:28:00Z","subjects":["ETD","Gamma-Weibull-G family of distributions","gamma-exponentiated modified Weibull distributions","statistical properties","uncertainty measure","Applied Statistics","Statistical Theory"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/1155","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Charles Champ","Daniel Linder"]},{"key":"dc:creator","label":"Author","values":["Pu, Shusen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2019-06-24T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis (restricted to Georgia Southern)"]},{"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","Gamma-Weibull-G family of distributions","gamma-exponentiated modified Weibull distributions","statistical properties","uncertainty measure","Applied Statistics","Statistical Theory"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/1155"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Weibull distribution and its extended families has been widely studied in lifetime applications. Based on the Weibull-G family of distributions and the exponentiated Weibull distribution, we study in detail two new classes of distributions, namely, Gamma-Weibull-G family of distributions (GWG) and gamma-exponentiated or generalized modified Weibull (GEMW) distribution. Some special models in these new classes are discussed. Statistical properties of these family of distributions, such as expansion of density function, hazard and reverse hazard functions, quantile function, moments, incomplete moments, generating functions, mean deviations, Bonferroni and Lorenz curves and order statistics are presented. For the GEMW, we also present Renyi entropy, estimation of parameters by using method of maximum likelihood, asymptotic confidence intervals and applications using real data.
"]},{"key":"dc:title","label":"Title","values":["Two New Classes of Generalized Modified Weibull Distributions with Application to Lifetime Data"]}]}],"canonical_facts":{"dc:contributor":["Charles Champ","Daniel Linder"],"dc:creator":["Pu, Shusen"],"dc:date.available":["2019-06-24T07:00:00Z"],"dc:description.abstract":["Weibull distribution and its extended families has been widely studied in lifetime applications. Based on the Weibull-G family of distributions and the exponentiated Weibull distribution, we study in detail two new classes of distributions, namely, Gamma-Weibull-G family of distributions (GWG) and gamma-exponentiated or generalized modified Weibull (GEMW) distribution. Some special models in these new classes are discussed. Statistical properties of these family of distributions, such as expansion of density function, hazard and reverse hazard functions, quantile function, moments, incomplete moments, generating functions, mean deviations, Bonferroni and Lorenz curves and order statistics are presented. For the GEMW, we also present Renyi entropy, estimation of parameters by using method of maximum likelihood, asymptotic confidence intervals and applications using real data.
"],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/1155"],"dc:subject":["ETD","Gamma-Weibull-G family of distributions","gamma-exponentiated modified Weibull distributions","statistical properties","uncertainty measure","Applied Statistics","Statistical Theory"],"dc:title":["Two New Classes of Generalized Modified Weibull Distributions with Application to Lifetime Data"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (restricted to Georgia Southern)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:28:00Z"}