Bayesian Parameter Estimation for the Birnbaum-Saunders Distribution and its Extension

We utilize the Bayesian approach to estimate the parameters of the Birnbaum-Saunders (BS) distribution devised by Birnbaum and Saunders (1969a), as well as the Generalized Birnbaum-Saunders (GBS) distribution obtained by Owen (2006), in the presence of random right censored data. We also derive the classical MLE expressions for the observed Information matrix of the GBS distribution, in order to illustrate the fact that no closed form expressions are available for the MLE, and numerical approximations are required to obtain the point estimates and asymptotic confidence intervals. Where Bayesian approach is concerned, new sets of priors are considered based on the model assumptions adopted by Birnbaum and Saunders (1969a) and Owen (2006). To handle the presence of random right censored observations, we utilize the data augmentation technique introduced by Tanner and Wong (1987), to circumvent the arduous expressions involving the censored data in obtaining posterior inferences. Simulation studies were carried out to assess performance of these methods under different parameter values, with small and large sample sizes, as well as various degrees of censoring. Two illustrative examples and some concluding remarks were finally presented