Mixture of Extended Birnbaum-Saunders Distributions: An Approach via the Mean-Mixture of Normal Models

The Birnbaum-Saunders (BS) distribution is one of the most con- sidered right-skewed distributions to model failure times for materials subject to lifetime data. In this paper, a new extension of the BS model is initially pro- posed based on the family of mean-mixtures of normal distributions. Then, we present a new probabilistic mixture model based on the new extended BS dis- tribution for modeling and clustering right-skewed and heavy-tailed data. The maximum likelihood (ML) parameter estimates of the model in question are 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 performance of the proposed methodology.