On bivariate Weibull-Geometric distribution

Abstract

Marshall and Olkin (1997) [14] provided a general method to introduce a parameter into a family of distributions and discussed in details about the exponential and Weibull families. They have also briefly introduced the bivariate extension, although not any properties or inferential issues have been explored, mainly due to analytical intractability of the general model. In this paper we consider the bivariate model with a special emphasis on the Weibull distribution. We call this new distribution as the bivariate Weibull-Geometric distribution. We derive different properties of the proposed distribution. This distribution has five parameters, and the maximum likelihood estimators cannot be obtained in closed form. We propose to use the EM algorithm, and it is observed that the implementation of the EM algorithm is quite straightforward. Two data sets have been analyzed for illustrative purposes, and it is observed that the new model and the proposed EM algorithm work quite well in these cases.