Bayesian inference of bivariate Weibull geometric model based on LINEX and quadratic loss functions

The bivariate Weibull-Geometric (BWG) distribution has been proposed by Kundu and Gupta (J Multivar Anal 123:19-29, 2014). They derived different properties of the proposed distribution and computing the maximum likelihood estimators via the expectation-maximization algorithm. The Bayes estimators of the parameters from the BWG distribution based on the squared error loss function (symmetric) and linear-exponential (LINEX) loss function (asymmetric), using informative and non-informative gamma priors are presented. Since the Bayes estimators of the mentioned distribution with five parameters cannot be obtained in explicit forms; the Gibbs sampler procedure is opted to achieve the Bayes estimators. Markov Chain Monte Carlo (MCMC) methods are broadly used to implement and compute the Bayes estimates. The convergence of the Markov chain to a stationary distribution has also been considered in detail. The associated credible intervals, namely the highest posterior density of the unknown parameters, are also constructed. The Monte Carlo simulations are done to compare different estimates. Finally, a real data set is considered to perform for illustrative purposes.