Bayes Estimation for the Block and Basu Bivariate and Multivariate Weibull Distributions

Block and Basu bivariate exponential distribution is one of the most popular absolute continuous bivariate distributions. Recently, Kundu and Gupta (‘A class of absolute continuous bivariate distributions’, Statistical Methodology, 2010) introduced Block and Basu bivariate Weibull distribution, which is a generalization of the Block and Basu bivariate exponential distribution, and provided the maximum likelihood estimators using EM algorithm. In this paper we consider the Bayesian inference of the unknown parameters of the Block and Basu bivariate Weibull distribution. The Bayes estimators are obtained with respect to the squared error loss function, and the prior distributions allow for prior dependence among the unknown parameters. Prior independence also can be obtained as a special case. It is observed that the Bayes estimators of the unknown parameters cannot be obtained in explicit forms. We propose to use the importance sampling technique to compute the Bayes estimates and also to construct the associated highest posterior density credible intervals. The analysis of two data sets have been performed for illustrative purposes. The performances of the proposed estimators are quite satisfactory. Finally we generalize the results for the multivariate case.