A new general class of discrete bivariate distributions constructed by using the likelihood ratio

Abstract

In statistics, stochastic orders formalize such a concept that one random variable is bigger than another. In this paper, we develop a new class of discrete bivariate distributions based on a stochastic order defined by the likelihood ratio. We derive general formula for the joint distributions belonging to the class. It will be seen that, from the proposed class, specific families of distributions can be efficiently generated just by specifying the ‘baseline seed distributions’. An important feature of the proposed discrete bivariate model is that, unlike other discrete bivariate models already proposed in the literature such as the well-known and most popular bivariate Poisson distribution by Holgate, it can model both positive and negative dependence. A number of new families of discrete bivariate distributions are generated from the proposed class. Furthermore, the generated bivariate distributions are applied to analyze real data sets and the results are compared with those obtained from some conventional models. © 2017, Springer-Verlag GmbH Germany, part of Springer Nature.