ABSTRACT

This chapter deals with two distinct types of bivariate distributions. The first class have been recently developed to describe the joint distributions of accidents incurred by individuals in consecutive time intervals under assumptions not common to the standard distributions considered in the earlier chapters. The second class of distributions have been introduced with a view to unifying some of the bivariate discrete distribution theory. Unfortunately, the two classes share little other than that the literature is sparse and the applications limited. The common component to them is the appearance of special functions of applied mathematics. From the development of the bivariate distributions discussed in the preceding chapters, it is obvious that they share a common genesis arising sometimes as a limiting form of the standard sampling schemes with or without replacement. In other instances they are constructed by the process of compounding or generalizing. In this chapter we will introduce new models and a unifying knot to tie them together.