On absolutely continuous bivariate generalized exponential power series distribution

Recently Mahmoudi and Jafari (2012) introduced generalized exponential power series distributions by compounding generalized exponential with the power series distributions. This is a very flexible distribution with some interesting physical interpretation. Kundu and Gupta (2011) introduced an absolute continuous bivariate generalized exponential distribution, whose marginals are generalized exponential distributions. The main aim of this paper is to introduce bivariate generalized exponential power series distributions. Two special cases namely bivariate generalized exponential geometric and bivariate generalized exponential Poisson distributions are discussed in details. It is observed that both the special cases are very flexible and their joint probability density functions can take variety of shapes. They have interesting copula structures and these can be used to study their different dependence structures and to compute different dependence measures. It is observed that both the models have six unknown parameters each, and the maximum likelihood estimators cannot be obtained in closed form. We have proposed to use EM algorithm to compute the maximum likelihood estimators of the unknown parameters. Some simulation experiments have been performed to see the effectiveness of the proposed EM algorithm. The analyses of two data sets have been performed for illustrative purposes, and it is observed that the proposed models and the EM algorithm work quite satisfactorily. Finally we provide the multivariate generalization of the proposed model.