Date of Award

Summer 2010

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Statistics

Program/Concentration

Computational and Applied Mathematics

Committee Director

Norou Diawara

Committee Member

Dayanand N. Naik

Committee Member

Larry D. Lee

Committee Member

Cynthia M. Jones

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.

DOI

10.25777/jgbf-4g75

ISBN

9781124291598

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