Absolute continuous bivariate generalized exponential distribution

Generalized exponential distribution has been used quite effectively to model positively skewed lifetime data as an alternative to the well known Weibull or gamma distributions. In this paper we introduce an absolute continuous bivariate generalized exponential distribution by using a simple transformation from a well known bivariate exchangeable distribution. The marginal distributions of the proposed bivariate generalized exponential distributions are generalized exponential distributions. The joint probability density function and the joint cumulative distribution function can be expressed in closed forms. It is observed that the proposed bivariate distribution can be obtained using Clayton copula with generalized exponential distribution as marginals. We derive different properties of this new distribution. It is a five-parameter distribution, and the maximum likelihood estimators of the unknown parameters cannot be obtained in closed forms. We propose some alternative estimators, which can be obtained quite easily, and they can be used as initial guesses to compute the maximum likelihood estimates. One data set has been analyzed for illustrative purposes. Finally we propose some generalization of the proposed model.