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.
Kundu, Debasis; Sarhan, Ammar; and D. Gupta, Rameshwar
"On Sarhan-Balakrishnan Bivariate Distribution,"
Journal of Statistics Applications & Probability: Vol. 1
, Article 2.
Available at: https://dc.naturalspublishing.com/jsap/vol1/iss3/2