Estimation of extreme percentiles in Birnbaum–Saunders distributions

The Birnbaum–Saunders distribution has recently received considerable attention in the statistical literature, including some applications in the environmental sciences. Several authors have generalized this distribution, but these generalizations are still inadequate for predicting extreme percentiles. In this paper, we consider a variation of the Birnbaum–Saunders distribution, which enables the prediction of extreme percentiles as well as the implementation of the EM algorithm for maximum likelihood estimation of the distribution parameters. This implementation has some advantages over the direct maximization of the likelihood function. Finally, we present results of a simulation study along with an application to a real environmental data set.