Authors

• Ali Akbar Jafari ¹
• Rasool Roozegar ¹
• Debasis Kundu ²

¹ Department of Statistics, Yazd University, Yazd, Iran

² Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Pin 208016, India

Abstract

In this paper, we introduce a new class of bivariate distributions by compounding the bivariate generalized exponential and power-series distributions. This new class contains the bivariate generalized exponential-Poisson, bivariate generalized exponential-logarithmic, bivariate generalized exponential-binomial and bivariate generalized exponential-negative binomial distributions as special cases. We derive different properties of the proposed class of distributions. It is observed that the proposed class of bivariate distributions is a very flexible class of distribution functions. The joint probability density functions can have a variety of shapes. It can be bimodal as well as heavy tailed also. This distribution has five parameters. The maximum likelihood estimators of the parameters cannot be obtained in closed form. We propose to use EM algorithm to compute the maximum likelihood estimators of the unknown parameters. It is observed that the proposed EM algorithm can be implemented very easily in practice. One data-set has been analyzed for illustrative purposes. It is observed that the proposed model and the EM algorithm work quite well in practice. 

Keywords

• Generalized exponential‎
• ‎Power series distributions‎
• ‎Bivariate distribution‎
• ‎Maximum likelihood estimator‎
• ‎EM algorithm‎