Bayesian Estimation for the Birnbaum-Saunders distribution in the presence of censored data

The use of Birnbaum-Saunders distribution can be a good alternative for analyzing data lifetime of equipment. In this work two different prior distributions are used in the estimation of the parameters of the Birnbaum-Saunders distribution under the Bayesian approach and with the presence of type I and II censored data. Assuming a priori dependence between parameters, an alternative prior distribution based on copula functions is proposed. Thus, a study to determine whether the priors lead to the same inference a posteriori is of great practical interest. Two examples are presented to illustrate the proposed methodology and investigated the performance of prior distributions. The Bayesian analysis is performed based on Monte Carlo Markov Chain (MCMC) to generate samples from the posterior distribution.