A Characterization of the Generalized Birnbaum–Saunders Distribution

Abstract

The Birnbaum–Saunders (BS) model is a fatigue life distribution related to the normal one with appealing properties. It is a non-negative transformation of a N(0,1) random variable Z, and its extended version, the so-called generalized Birnbaum– Saunders (GBS) model, obtained replacing Z by any other symmetric continuous random variable, shares the same properties. In this paper we characterize the GBS distribution according to one of its outstanding properties and take advantage of this characterization to derive a graphical procedure to assess whether an observed data set follows a GBS distribution. We further develop a goodness-of-fit test for the hypothesis that the data follow a BS distribution with unknown parameters and apply the results to real data sets.