Date of Award
Doctor of Philosophy
Kenneth J. Koehler
We review some methods of constructing bivariate and multivariate distributions with given margins. When the margins are assumed known, we present a new method of deriving multivariate distributions based on a conditional approach that allows for different associations between different pairs of variables. Some general properties are examined and this method is illustrated by generalizing the Clayton (1978), Plackett (1965), and Lindley and Singpurwalla (1986) distributions. This method of construction provides a convenient way to simulate random samples from multivariate distributions, and an algorithm is presented;This methodology is used to model a data set from a teratological study. The generalized Clayton distribution is used to model the joint distribution of incisor eruption times for litter mates including two male rats and one female rat. The marginal distribution of incisor eruption of each individual is modeled by a proportional hazards model with a Weibull baseline hazard function. Maximum likelihood estimates are computed for the parameters, and the results are discussed;In Chapter 4 we present an alternative method of constructing multivariate distributions with specific univariate marginal distributions obtained from solving a Cauchy type partial differential equation whose solutions involve the Bessel function of order zero. Many distributions are shown to be special cases of a family of distributions arising from a certain solution. Some of the properties of this family are derived. New families of bivariate distributions are derived;In Chapter 5, we introduce a randomization technique to extend families of multivariate distributions. Families of bivariate distributions that allow for only positive associations, for example, are extended to families with unrestricted correlations. When the marginals are defined on symmetric intervals we randomize using a binomial distribution. This results in bivariate distributions with a symmetric range for possible correlations and an extended variety of shapes. In the more general case, we randomize on the copulas associated with the distributions. Finally, we examine the case where the randomizing distribution is continuous.
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/
Chakak, Abderrahmane, "Some methods of constructing multivariate distributions " (1993). Retrospective Theses and Dissertations. 10411.