A NOTE ON THE BIVARIATE GENERALIZED POISSON DISTRIBUTION OF TYPE 1

Given the univariate generalized Poisson distribution as defined by Déniz and Sarabia [5], in this paper, we construct a bivariate generalized Poisson distribution of type 1 whose marginal distributions are univariate generalized Poisson distributions according to Déniz and Sarabia [5]. We also show that this distribution belongs to the family of bivariate Poisson distributions. Under certain conditions, this distribution converges in distribution to the bivariate Poisson distribution of Berkhout and Plug [4]. It also converges to the bivariate Poisson distribution of Lakshminarayana et al. [9].