Mathematical Sciences: Multivariate Distribution Theory

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This research has two components. One is to systematically study mixture models for multivariate distributions, as they arise naturally in physicaly settings, statistical derivations, and Bayesian analysis. These models often shed light on the applicability and properties of derived distributions. In addition, functional equation techniques are employed, particularly in the study of multivariate distributions with uniform marginals. The second component is to generalize reliability models. This research is in multivariate statistics and aims to create and characterize mathematical models which permit meaningful relationships between variables.