On bivariate and a mixture of bivariate Birnbaum–Saunders distributions

Abstract

Univariate Birnbaum–Saunders distribution has received a considerable amount of attention during the last few years. Recently, Kundu et al. (2010) introduced a bivariate Birnbaum–Saunders distribution. It is observed that the bivariate Birnbaum–Saunders distributions can be written as the weighted mixture of bivariate inverse Gaussian distribution and its reciprocals. In this paper further we introduce a mixture of two bivariate Birnbaum–Saunders distributions and discuss its different properties. The mixture model has eleven parameters, hence it is a very flexible model. The maximum likelihood estimators cannot be obtained in explicit forms. We propose to use the EM algorithm to compute the maximum likelihood estimators. It is observed that it saves computational time significantly. We performed some simulation experiments, and one data analysis has been performed to illustrate the EM algorithm. It is observed that the performance of the EM algorithm is quite satisfactory.