Mixture of extended Birnbaum-Saunders distributions: an approach via the mean-mixture of normal models

Abstract

The Birnbaum-Saunders (BS) distribution is one of the most con-sidered right-skewed distributions to model failure times for materials subjectto lifetime data. In this paper, a new extension of the BS model is initiallyproposed based on the family of mean-mixtures of normal distributions. Then,we present a new probabilistic mixture model based on the new extended BSdistribution for modeling and clustering right-skewed and heavy-tailed data.The maximum likelihood (ML) parameter estimates of the model in questionare estimated by employing an expectation-maximization (EM) type algorithm.Moreover, the empirical information matrix is derived by using an information-based approach. Simulations and real data analysis illustrate the performanceof the proposed methodology.