Abstract:In this paper we propose a new five parameter bivariate distribution obtained by taking geometric maximum of generalized exponential distributions. Several properties of this new bivariate distribution and its marginals have been investigated. It is observed that the maximum likelihood estimators of the unknown parameters cannot be obtained in closed form. Five non-linear equations need to be solved simultaneously to compute the maximum likelihood estimators of the unknown parameters. We propose to use the EM algorithm to compute the maximum likelihood estimators of the unknown parameters, and it is computationally quite tractable. We performed extensive simulations study to see the effectiveness of the proposed algorithm, and the performance is quite satisfactory. We analyze one data set for illustrative purposes. Finally we propose some open problems.