An EM algorithm for absolutely continuous Marshall-Olkin bivariate Pareto distribution with location and scale

Abstract

Block and Basu bivariate exponential distribution is one of the most popular absolutely continuous bivariate distributions. In this article, we have considered a Block–Basu type bivariate Pareto distribution. Here in the standard manner, first Marshall-Olkin type singular bivariate distribution has been constructed, and then by taking away the singular component similar to the Block and Basu model, an absolute continuous BB-BVPA model has been constructed. Further, the location and scale parameters also have been introduced. Therefore, the model has seven parameters. We drive different properties of this absolutely continuous distribution. Since the maximum likelihood estimators of the parameters cannot be expressed in a closed form, we propose to use an EM algorithm to compute the estimators of the model parameters. Some simulation experiments have been performed for illustrative purposes. We fit the model to rainfall data in the context of landslide risk estimation. The methods are implemented in the publicly available R package bvpa.