  In this paper we develop a bivariate discrete generalized exponential
distribution, whose marginals are discrete generalized exponential distribution
as proposed by Nekoukhou, Alamatsaz and Bidram ("Discrete generalized
exponential distribution of a second type", Statistics, 47, 876 - 887, 2013).
It is observed that the proposed bivariate distribution is a very flexible
distribution and the bivariate geometric distribution can be obtained as a
special case of this distribution. The proposed distribution can be seen as a
natural discrete analogue of the bivariate generalized exponential distribution
proposed by Kundu and Gupta ("Bivariate generalized exponential distribution",
Journal of Multivariate Analysis, 100, 581 - 593, 2009). We study different
properties of this distribution and explore its dependence structures. We
propose a new EM algorithm to compute the maximum likelihood estimators of the
unknown parameters which can be implemented very efficiently, and discuss some
inferential issues also. The analysis of one data set has been performed to
show the effectiveness of the proposed model. Finally we propose some open
problems and conclude the paper.
