The extreme value Birnbaum-Saunders model in athletics

Abstract

The Birnbaum-Saunders (BS) model is a life distribution that has recently been largely studied and applied. A random variable following the BS distribution can be defined through a simple transformation of a standard normal. The BS model can thus be generalized by switching the standard normal distribution of the basis random variable, allowing the construction of more general classes of models. Among those models, we mention the extreme value Birnbaum-Saunders (EVBS) models, recently introduced in the literature, and based on results from extreme value theory. A real application to athletics data will be used to illustrate the methodology and to provide the way this model and related models can link with traditional extreme value analysis methods.