Abstract:

In this paper, we introduce a new bivariate count distribution, called the Bivariate Extended Poisson distribution of type 3 (BEP3 distribution), constructed using the trivariate reduction method, which is widely used in the statistical literature to model positive dependence between discrete variables. This distribution accommodates both overdispersion or underdispersion and strictly positive dependence between two count variables. We study its main theoretical properties and estimate its parameters using the maximum likelihood method, based on an Expectation-Maximization (EM) algorithm. We compare the goodness-of-fit of the new distribution to that of other bivariate models for count data on two real-world datasets. The BEP3 distribution was found to provide a better fit than some of the models considered.