{"id":{"repo_id":"unr","oai_identifier":"oai:scholarwolf.unr.edu:11714/11556"},"canonical_url":"https://search.dev.ndltd.org/etd/unr/oai:scholarwolf.unr.edu:11714/11556","repository":{"repo_id":"unr","name":"University of Nevada - Reno","base_url":"https://scholarwolf.unr.edu/server/oai/request"},"display":{"title":"The joint distribution of the maximum and duration of stochastic events driven by Pareto II observations","abstract":"We study the joint distribution of X and N, where N has the geometric distribution and X is the maximum of the N independent and identically distributed Pareto II (Lomax) observations. The bivariate distribution is referred to as the geometric Marshall-Olkin Lomax distribution (GMOL). A related model for a geometric maximum of IID exponential observations was introduced by Kozubowski and Panorska (2008) and has proven useful in areas such as finance, hydrology and climate. However, the existence of heavy tails in environmental variables motivated this model. Our results for this research include derivations of the joint probability density function, cumulative distribution function, conditional and marginal distributions, conditional survival function, moment-generating function, Laplace transforms, and covariance matrix. We also address the problem of parameter estimation using the method of maximum likelihood. Estimation is empirically verified using a simulation study. We also present results of modeling precipitation and temperature data sets.","abstract_html":"We study the joint distribution of X and N, where N has the geometric distribution and X is the maximum of the N independent and identically distributed Pareto II (Lomax) observations. The bivariate distribution is referred to as the geometric Marshall-Olkin Lomax distribution (GMOL). A related model for a geometric maximum of IID exponential observations was introduced by Kozubowski and Panorska (2008) and has proven useful in areas such as finance, hydrology and climate. However, the existence of heavy tails in environmental variables motivated this model. Our results for this research include derivations of the joint probability density function, cumulative distribution function, conditional and marginal distributions, conditional survival function, moment-generating function, Laplace transforms, and covariance matrix. We also address the problem of parameter estimation using the method of maximum likelihood. Estimation is empirically verified using a simulation study. We also present results of modeling precipitation and temperature data sets.","abstract_has_math":false,"creators":["Donkor, Foster"],"institution":null,"degree_name":null,"degree_level":"Master's Degree","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Panorska, Anna K."],"committee_chairs":[],"committee_members":["Kozubowski, Tomasz J.","Lu, Minggen","Kemmelmeier, Markus"],"year":2025,"date_issued":"2025","date_published":"2025","updated_at":"2026-07-27T21:46:19Z","subjects":["GMOL Model","Heavy Tail","Lomax/Pareto Type II Distribution","Maximum Likelihood Estimation","Power Law","Precipitation Data"],"languages":["en_US","English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarwolf.unr.edu/handle/11714/11556","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Panorska, Anna K."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Kozubowski, Tomasz J.","Lu, Minggen","Kemmelmeier, Markus"]},{"key":"dc:creator","label":"Author","values":["Donkor, Foster"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2025-09-08T18:38:53Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2025-09-08T18:38:53Z"]},{"key":"dc:date.issued","label":"Date","values":["2025"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's Degree"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["GMOL Model","Heavy Tail","Lomax/Pareto Type II Distribution","Maximum Likelihood Estimation","Power Law","Precipitation Data"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://scholarwolf.unr.edu/handle/11714/11556"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We study the joint distribution of X and N, where N has the geometric distribution and X is the maximum of the N independent and identically distributed Pareto II (Lomax) observations. The bivariate distribution is referred to as the geometric Marshall-Olkin Lomax distribution (GMOL). A related model for a geometric maximum of IID exponential observations was introduced by Kozubowski and Panorska (2008) and has proven useful in areas such as finance, hydrology and climate. However, the existence of heavy tails in environmental variables motivated this model. Our results for this research include derivations of the joint probability density function, cumulative distribution function, conditional and marginal distributions, conditional survival function, moment-generating function, Laplace transforms, and covariance matrix. We also address the problem of parameter estimation using the method of maximum likelihood. Estimation is empirically verified using a simulation study. We also present results of modeling precipitation and temperature data sets."]},{"key":"dc:format","label":"Dc Format","values":["PDF"]},{"key":"dc:title","label":"Title","values":["The joint distribution of the maximum and duration of stochastic events driven by Pareto II observations"]}]}],"canonical_facts":{"dc:contributor.advisor":["Panorska, Anna K."],"dc:contributor.committeemember":["Kozubowski, Tomasz J.","Lu, Minggen","Kemmelmeier, Markus"],"dc:creator":["Donkor, Foster"],"dc:date.accessioned":["2025-09-08T18:38:53Z"],"dc:date.available":["2025-09-08T18:38:53Z"],"dc:date.issued":["2025"],"dc:description.abstract":["We study the joint distribution of X and N, where N has the geometric distribution and X is the maximum of the N independent and identically distributed Pareto II (Lomax) observations. The bivariate distribution is referred to as the geometric Marshall-Olkin Lomax distribution (GMOL). A related model for a geometric maximum of IID exponential observations was introduced by Kozubowski and Panorska (2008) and has proven useful in areas such as finance, hydrology and climate. However, the existence of heavy tails in environmental variables motivated this model. Our results for this research include derivations of the joint probability density function, cumulative distribution function, conditional and marginal distributions, conditional survival function, moment-generating function, Laplace transforms, and covariance matrix. We also address the problem of parameter estimation using the method of maximum likelihood. Estimation is empirically verified using a simulation study. We also present results of modeling precipitation and temperature data sets."],"dc:format":["PDF"],"dc:identifier.uri":["https://scholarwolf.unr.edu/handle/11714/11556"],"dc:language":["English"],"dc:language.iso":["en_US"],"dc:subject":["GMOL Model","Heavy Tail","Lomax/Pareto Type II Distribution","Maximum Likelihood Estimation","Power Law","Precipitation Data"],"dc:title":["The joint distribution of the maximum and duration of stochastic events driven by Pareto II observations"],"dc:type":["Thesis"],"thesis:degree_level":["Master's Degree"]},"updated_at":"2026-07-27T21:46:19Z"}