Generalized modified slash Birnbaum–Saunders distribution

Abstract

In this paper, a generalization of the modified slash Birnbaum-Saunders (BS) distribution is introduced. The model is defined by using the stochastic representation of the BS distribution, where the standard normal distribution is replaced by a symmetric distribution proposed by Reyes et al. It is proved that this new distribution is able to model more kurtosis than other extensions of BS previously proposed in the literature. Closed expressions are given for the pdf (probability density functio), along with their moments, skewness and kurtosis coefficients. Inference carried out is based on modified moments method and maximum likelihood (ML). To obtain ML estimates, two approaches are considered: Newton-Raphson and EM-algorithm. Applications reveal that it has potential for doing well in real problems.