Bayesian analysis of Birnbaum–Saunders distribution via the generalized ratio-of-uniforms method

© 2015, Springer-Verlag Berlin Heidelberg. This paper deals with the Bayesian inference for the parameters of the Birnbaum–Saunders distribution. We adopt the inverse-gamma priors for the shape and scale parameters because the continuous conjugate joint prior distribution does not exist and the reference prior (or independent Jeffreys’ prior) results in an improper posterior distribution. We propose an efficient sampling algorithm via the generalized ratio-of-uniforms method to compute the Bayesian estimates and the credible intervals. One appealing advantage of the proposed procedure over other sampling techniques is that it efficiently generates independent samples from the required posterior distribution. Simulation studies are conducted to investigate the behavior of the proposed method, and two real-data applications are analyzed for illustrative purposes