In this paper we studied a three-parameter absolutely continuous bivariate distribution whose marginals are generalized exponential distributions. The proposed three-parameter bivariate distribution can be used quite effectively as an alternative to the Block and Basu bivariate exponential distribution. The joint probability den- sity function, the joint cumulative distribution function and its associated copula have simple forms. We derive different properties of this new distribution. The maximum likelihood estimators of the unknown parameters can be obtained by solving simul-taneously three non-linear equations. We propose to use EM algorithm to compute the maximum likelihood estimators, which can be implemented quite conveniently. One data set has been analyzed for illustrative purposes. Finally we propose some generalization of the proposed model

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