Journal of Statistics Applications & Probability

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Recently Sarhan and Balakrishnan (Journal of Multivariate Analysis, 98, 1508 - 1527, 2007) introduced a new singular bivariate distribution using generalized exponential and exponential distributions. They discussed several interesting properties of this new distribution. Sarhan-Balakrishnan did not discuss any estimation procedure of the unknown parameters. In Sarhan-Balakrishnan model, there is no scale parameter. Unfortunately without the presence of any scale parameter, it is difficult to use it for any data analysis purposes. We introduce a scale parameter in the model and it becomes a four-parameter bivariate model. The usual maximum likelihood calculation involves a four dimensional optimization problem. We discuss the maximum likelihood estimation of the unknown parameters using EM algorithm, and it involves only a one-dimensional optimization calculation at each M-step of the EM algorithm. One data analysis has been performed for illustrative purposes. The performance of the EM algorithm is very satisfactory.

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