A Bivariate Conway-Maxwell Poisson Distribution

摘要

This thesis explores the development and evaluates the properties of a bivari- ate Conway-Maxwell Poisson (bCMP) distribution obtained via trivariate reduction. While not as common in literature as the univariate Poisson, the univariate CMP is still well documented and widely used to address the problem of data dispersion. Our purpose here is to extend the flexibility and utility of the univariate CMP to a bivariate form.;A brief history of the development of the CMP is provided, with examples of related distributions for comparison. After this, a bivariate CMP distribution will be derived from the univariate form using the method of trivariate reduction, with a full description of the moments and special cases encompassed within the distribution. A method for estimation of parameters will also be explored.