In this thesis, new classes of Weibull and inverse Weibull distributions including the generalized new modified Weibull (GNMW), gamma-generalized inverse Weibull (GGIW), the weighted proportional inverse Weibull (WPIW) and inverse new modified Weibull (INMW) distributions are introduced. The GNMW contains several sub-models including the new modified Weibull (NMW), generalized modified Weibull (GMW), modified Weibull (MW), Weibull (W) and exponential (E) distributions, just to mention a few. The class of WPIW distributions contains several models such as: length-biased, hazard and reverse hazard proportional inverse Weibull, proportional inverse Weibull, inverse Weibull, inverse exponential, inverse Rayleigh, and Frechet distributions as special cases. Included in the GGIW distribution are the sub-models: gamma-generalized inverse Weibull, gamma-generalized Frechet, gamma-generalized inverse Rayleigh, gamma-generalized inverse exponential, inverse Weibull, inverse Rayleigh, inverse exponential, Frechet distributions. The INMW distribution contains several sub-models including inverse Weibull, inverse new modified exponential, inverse new modified Rayleigh, new modified Frechet, inverse modified Weibull, inverse Rayleigh and inverse exponential distributions as special cases. Properties of these distributions including the behavior of the hazard function, moments, coefficients of variation, skewness, and kurtosis, s-entropy, distribution of order statistic and Fisher information are presented. Estimates of the parameters of the models via method of maximum likelihood (ML) are presented. Extensive simulation study is conducted and numerical examples are given.
","abstract_html":"<p>In this thesis, new classes of Weibull and inverse Weibull distributions including the generalized new modified Weibull (GNMW), gamma-generalized inverse Weibull (GGIW), the weighted proportional inverse Weibull (WPIW) and inverse new modified Weibull (INMW) distributions are introduced. The GNMW contains several sub-models including the new modified Weibull (NMW), generalized modified Weibull (GMW), modified Weibull (MW), Weibull (W) and exponential (E) distributions, just to mention a few. The class of WPIW distributions contains several models such as: length-biased, hazard and reverse hazard proportional inverse Weibull, proportional inverse Weibull, inverse Weibull, inverse exponential, inverse Rayleigh, and Frechet distributions as special cases. Included in the GGIW distribution are the sub-models: gamma-generalized inverse Weibull, gamma-generalized Frechet, gamma-generalized inverse Rayleigh, gamma-generalized inverse exponential, inverse Weibull, inverse Rayleigh, inverse exponential, Frechet distributions. The INMW distribution contains several sub-models including inverse Weibull, inverse new modified exponential, inverse new modified Rayleigh, new modified Frechet, inverse modified Weibull, inverse Rayleigh and inverse exponential distributions as special cases. Properties of these distributions including the behavior of the hazard function, moments, coefficients of variation, skewness, and kurtosis, s-entropy, distribution of order statistic and Fisher information are presented. Estimates of the parameters of the models via method of maximum likelihood (ML) are presented. Extensive simulation study is conducted and numerical examples are given.</p>","abstract_has_math":false,"creators":["Sherina, Valeriia"],"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 W. 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":"2026-07-24T02:28:00Z","subjects":["ETD","Proportional Inverse Weibull Distribution","Generalized Inverse Weibull Distribution","Weighted distribution","New modified Wiebull distribution","Applied Statistics","Statistical Models","Statistical Theory"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/1149","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Charles W. Champ","Arpita Chatterjee"]},{"key":"dc:creator","label":"Author","values":["Sherina, Valeriia"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2019-07-30T07:00:00Z"]},{"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","Proportional Inverse Weibull Distribution","Generalized Inverse Weibull Distribution","Weighted distribution","New modified Wiebull distribution","Applied Statistics","Statistical Models","Statistical Theory"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/1149"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, new classes of Weibull and inverse Weibull distributions including the generalized new modified Weibull (GNMW), gamma-generalized inverse Weibull (GGIW), the weighted proportional inverse Weibull (WPIW) and inverse new modified Weibull (INMW) distributions are introduced. The GNMW contains several sub-models including the new modified Weibull (NMW), generalized modified Weibull (GMW), modified Weibull (MW), Weibull (W) and exponential (E) distributions, just to mention a few. The class of WPIW distributions contains several models such as: length-biased, hazard and reverse hazard proportional inverse Weibull, proportional inverse Weibull, inverse Weibull, inverse exponential, inverse Rayleigh, and Frechet distributions as special cases. Included in the GGIW distribution are the sub-models: gamma-generalized inverse Weibull, gamma-generalized Frechet, gamma-generalized inverse Rayleigh, gamma-generalized inverse exponential, inverse Weibull, inverse Rayleigh, inverse exponential, Frechet distributions. The INMW distribution contains several sub-models including inverse Weibull, inverse new modified exponential, inverse new modified Rayleigh, new modified Frechet, inverse modified Weibull, inverse Rayleigh and inverse exponential distributions as special cases. Properties of these distributions including the behavior of the hazard function, moments, coefficients of variation, skewness, and kurtosis, s-entropy, distribution of order statistic and Fisher information are presented. Estimates of the parameters of the models via method of maximum likelihood (ML) are presented. Extensive simulation study is conducted and numerical examples are given.
"]},{"key":"dc:title","label":"Title","values":["Generalized Weibull and Inverse Weibull Distributions with Applications"]}]}],"canonical_facts":{"dc:contributor":["Charles W. Champ","Arpita Chatterjee"],"dc:creator":["Sherina, Valeriia"],"dc:date.available":["2019-07-30T07:00:00Z"],"dc:description.abstract":["In this thesis, new classes of Weibull and inverse Weibull distributions including the generalized new modified Weibull (GNMW), gamma-generalized inverse Weibull (GGIW), the weighted proportional inverse Weibull (WPIW) and inverse new modified Weibull (INMW) distributions are introduced. The GNMW contains several sub-models including the new modified Weibull (NMW), generalized modified Weibull (GMW), modified Weibull (MW), Weibull (W) and exponential (E) distributions, just to mention a few. The class of WPIW distributions contains several models such as: length-biased, hazard and reverse hazard proportional inverse Weibull, proportional inverse Weibull, inverse Weibull, inverse exponential, inverse Rayleigh, and Frechet distributions as special cases. Included in the GGIW distribution are the sub-models: gamma-generalized inverse Weibull, gamma-generalized Frechet, gamma-generalized inverse Rayleigh, gamma-generalized inverse exponential, inverse Weibull, inverse Rayleigh, inverse exponential, Frechet distributions. The INMW distribution contains several sub-models including inverse Weibull, inverse new modified exponential, inverse new modified Rayleigh, new modified Frechet, inverse modified Weibull, inverse Rayleigh and inverse exponential distributions as special cases. Properties of these distributions including the behavior of the hazard function, moments, coefficients of variation, skewness, and kurtosis, s-entropy, distribution of order statistic and Fisher information are presented. Estimates of the parameters of the models via method of maximum likelihood (ML) are presented. Extensive simulation study is conducted and numerical examples are given.
"],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/1149"],"dc:subject":["ETD","Proportional Inverse Weibull Distribution","Generalized Inverse Weibull Distribution","Weighted distribution","New modified Wiebull distribution","Applied Statistics","Statistical Models","Statistical Theory"],"dc:title":["Generalized Weibull and Inverse Weibull Distributions with Applications"],"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":"2026-07-24T02:28:00Z"}