Modelling discrete bivariate data with applications to failure and count data

In this study, we propose a new class of flexible bivariate distributions for discrete random variables. The proposed class of distribution is based on the notion of conditional failure rate for a discrete type random variable. We derive general formulae for the joint distributions belonging to the proposed class that, unlike other discrete bivariate models already proposed in the literature such as the well-known and most popular bivariate Poisson distribution by Holgate1, can model both positive and negative dependence. We discuss general statistical properties of the proposed class as well. Specific families of bivariate distributions can be generated from the general class proposed in this paper just by specifying the 'baseline distributions'. Furthermore, specific discrete bivariate distributions belonging to the proposed class are applied to analyze three real data sets and the results are compared with those obtained from conventional models.