{"id":{"repo_id":"gsu","oai_identifier":"oai:digitalcommons.georgiasouthern.edu:etd-1665"},"canonical_url":"https://search.dev.ndltd.org/etd/gsu/oai:digitalcommons.georgiasouthern.edu:etd-1665","repository":{"repo_id":"gsu","name":"Georgia Southern University","base_url":"https://digitalcommons.georgiasouthern.edu/do/oai/"},"display":{"title":"Theoretical Properties and Estimation In Weighted Weibull and Related Distributions","abstract":"The Weibull distribution is a well known and common distribution. In this thesis, theoretical properties of weighted Weibull distributions are presented. Properties of the non-weighted Weibull distribution are also reiterated for comparison. The probability density functions, cumulative distribution functions, survival functions, hazard functions and reverse hazard functions are given for each distribution. In addition, Glaser's Lemma is applied to determine the behavior of the hazard functions. The standardized moments, differential entropy, Fisher information and results based on the likelihood function are given for each distribution as well. These results are also shown for the Rayleigh distribution, a special case of the Weibull distribution, and its weighted versions.","abstract_html":"The Weibull distribution is a well known and common distribution. In this thesis, theoretical properties of weighted Weibull distributions are presented. Properties of the non-weighted Weibull distribution are also reiterated for comparison. The probability density functions, cumulative distribution functions, survival functions, hazard functions and reverse hazard functions are given for each distribution. In addition, Glaser's Lemma is applied to determine the behavior of the hazard functions. The standardized moments, differential entropy, Fisher information and results based on the likelihood function are given for each distribution as well. These results are also shown for the Rayleigh distribution, a special case of the Weibull distribution, and its weighted versions.","abstract_has_math":false,"creators":["Roman, Ryan"],"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":"2010-07-01T07:00:00Z","date_published":"2010-07-01T07:00:00Z","updated_at":"2026-07-24T02:27:19Z","subjects":["ETD","Weighted distribution","Weibull distribution","Weighted Weibull distribution","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/665","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":["Roman, Ryan"]}]},{"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","Weighted distribution","Weibull distribution","Weighted Weibull distribution","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/665"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The Weibull distribution is a well known and common distribution. In this thesis, theoretical properties of weighted Weibull distributions are presented. Properties of the non-weighted Weibull distribution are also reiterated for comparison. The probability density functions, cumulative distribution functions, survival functions, hazard functions and reverse hazard functions are given for each distribution. In addition, Glaser's Lemma is applied to determine the behavior of the hazard functions. The standardized moments, differential entropy, Fisher information and results based on the likelihood function are given for each distribution as well. These results are also shown for the Rayleigh distribution, a special case of the Weibull distribution, and its weighted versions."]},{"key":"dc:title","label":"Title","values":["Theoretical Properties and Estimation In Weighted Weibull and Related Distributions"]}]}],"canonical_facts":{"dc:contributor":["Charles Champ","Hani Samawi"],"dc:creator":["Roman, Ryan"],"dc:date.available":["2013-10-17T07:00:00Z"],"dc:description.abstract":["The Weibull distribution is a well known and common distribution. In this thesis, theoretical properties of weighted Weibull distributions are presented. Properties of the non-weighted Weibull distribution are also reiterated for comparison. The probability density functions, cumulative distribution functions, survival functions, hazard functions and reverse hazard functions are given for each distribution. In addition, Glaser's Lemma is applied to determine the behavior of the hazard functions. The standardized moments, differential entropy, Fisher information and results based on the likelihood function are given for each distribution as well. These results are also shown for the Rayleigh distribution, a special case of the Weibull distribution, and its weighted versions."],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/665"],"dc:subject":["ETD","Weighted distribution","Weibull distribution","Weighted Weibull distribution","Mathematics"],"dc:title":["Theoretical Properties and Estimation In Weighted Weibull 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":"2026-07-24T02:27:19Z"}