On an extreme value version of the Birnbaum-Saunders distribution

Abstract

The Birnbaum-Saunders model is a life distribution originated from a problem of material fatigue that has been largely studied and applied in recent decades. A random variable following the Birnbaum-Saunders distribution can be stochastically represented by another random variable used as basis. Then, the Birnbaum-Saunders model can be generalized by switching the distribution of the basis variable using diverse arguments allowing to construct more general classes of models. Extreme value distributions are useful to determinate the probability of events that are more extreme than any that have already been observed. In this paper, we propose, characterize, implement and apply an extreme value version of the Birnbaum-Saunders distribution.