Absolute Continuous Multivariate Generalized Exponential Distribution

Generalized exponential distribution has received some attention in the last few years. Recently Kundu and Gupta (2011) and Shoaee and Khorram (2012) introduced an absolute continuous bivariate generalized exponential distribution. In this paper we propose an absolute continuous multivariate generalized exponential distribution. The proposed distribution is very flexible, and the joint probability density functions can take different shapes. We provide several properties of this model. Further, it is observed that the multivariate generalized exponential model can be obtained using multivariate Clayton copula. The maximum likelihood estimators are quite difficult to compute in practice. Due to this reason, we propose two step estimation procedure using the copula approach, which are quite easy to implement. Simulation experiments are performed to compare the performances of the two different estimators, and the performances are quite similar in nature particularly for large sample sizes. One multivariate bone mineral density data set has been analyzed for illustrative purposes, and it is observed that the proposed model provides a very good fit to the data set.