Because of the numerous applications, characterization of multivariate survival distributions is still a growing area of research. The aim of this thesis is to investigate a joint probability distribution that can be derived for modeling nonnegative related random variables. We restrict the marginals to a specified lifetime distribution, while proposing a linear relationship between them with an unknown (error) random variable that we completely characterize. The distributions are all of positive supports, but one class has a positive probability of simultaneous occurrence. In that sense, we capture the absolutely continuous case, and the Marshall-Olkin type with a positive probability of simultaneous event on a set of measure zero. In particular, the form of the joint distribution when the marginals are of gamma distributions are provided, combining in a simple parametric form the dependence between the two random variables and a nonparametric likelihood function for the unknown random variable. Associated properties are studied and investigated and applications with simulated and real data are given.
","abstract_html":"<p>Because of the numerous applications, characterization of multivariate survival distributions is still a growing area of research. The aim of this thesis is to investigate a joint probability distribution that can be derived for modeling nonnegative related random variables. We restrict the marginals to a specified lifetime distribution, while proposing a linear relationship between them with an unknown (error) random variable that we completely characterize. The distributions are all of positive supports, but one class has a positive probability of simultaneous occurrence. In that sense, we capture the absolutely continuous case, and the Marshall-Olkin type with a positive probability of simultaneous event on a set of measure zero. In particular, the form of the joint distribution when the marginals are of gamma distributions are provided, combining in a simple parametric form the dependence between the two random variables and a nonparametric likelihood function for the unknown random variable. Associated properties are studied and investigated and applications with simulated and real data are given.</p>","abstract_has_math":false,"creators":["Indika, S. H. Sathish"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["Norou Diawara","Dayanand N. Naik","Larry D. Lee","Cynthia M. Jones"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-07-01T07:00:00Z","date_published":"2010-07-01T07:00:00Z","updated_at":"2026-07-24T03:34:53Z","subjects":["Bivariate survival data","Likelihood functions","Sequential estimation","Mathematics","Statistics and Probability"],"languages":[],"rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
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"]},{"key":"dc:title","label":"Title","values":["Semi-Parametric Likelihood Functions for Bivariate Survival Data"]}]}],"canonical_facts":{"dc:contributor":["Norou Diawara","Dayanand N. Naik","Larry D. Lee","Cynthia M. Jones"],"dc:creator":["Indika, S. H. Sathish"],"dc:date.available":["2019-06-05T07:00:00Z"],"dc:description.abstract":["Because of the numerous applications, characterization of multivariate survival distributions is still a growing area of research. The aim of this thesis is to investigate a joint probability distribution that can be derived for modeling nonnegative related random variables. We restrict the marginals to a specified lifetime distribution, while proposing a linear relationship between them with an unknown (error) random variable that we completely characterize. The distributions are all of positive supports, but one class has a positive probability of simultaneous occurrence. In that sense, we capture the absolutely continuous case, and the Marshall-Olkin type with a positive probability of simultaneous event on a set of measure zero. In particular, the form of the joint distribution when the marginals are of gamma distributions are provided, combining in a simple parametric form the dependence between the two random variables and a nonparametric likelihood function for the unknown random variable. Associated properties are studied and investigated and applications with simulated and real data are given.
"],"dc:identifier":["9781124291598","https://digitalcommons.odu.edu/mathstat_etds/30"],"dc:rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"dc:subject":["Bivariate survival data","Likelihood functions","Sequential estimation","Mathematics","Statistics and Probability"],"dc:title":["Semi-Parametric Likelihood Functions for Bivariate Survival Data"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:34:53Z"}