Birnbaum–Saunders Distribution Based on Asymmetric Heavy-Tailed Distributions, Associated Inference, and Application

Birnbaum–Saunders (BS) distribution has received considerable attention in the statistical literature, both in applied and theoretical problems. Even though much work has been done on extensions of the BS distribution, there is still a need for models for predicting extreme percentiles and for fitting data that are highly concentrated on the left-tail of the distribution. This article proposes a robust extension of the BS distribution, based on scale mixtures of skew-normal distributions that can be used to model highly asymmetric data. This extension provides flexible heavy-tailed distributions which can be used in the robust estimation of parameters in the presence of outlying observations, as well as an EM-algorithm for the maximum likelihood estimation of model parameters. Finally, the proposed model and methods of inference are examined and illustrated by means of Monte Carlo simulation studies and a real data set.