ABSTRACT
In this chapter we shall be considering the basic properties of bivariate discrete distributions. As is well known, central to the study of probability distributions is the generating function. In the case of discrete distributions, the probability generating function plays a vital role as, in most of the situations, it is much simpler to handle than is the moment generating function. However, in addition to the probability generating function we will define a variety of generating functions of which the importance and usefulness will be made clear in the context in which they appear. The relationships between the different types of moments will also be developed. The structure of bivariate discrete distributions has been studied by several authors by a canonical representation. These ideas will be introduced in this chapter. Specifics will be referred to a later section appropriate to the distribution under consideration. Finally, the computer age has been instrumental in making the abstraction of theory a reality. To this end, some general ideas concerning the computer generation of random samples from bivariate discrete distributions will also be presented in this chapter with, once again, the specifics being left to be given in the appropriate sections.
