Generalized Birnbaum-Saunders Distribution

The two-parameter Birnbaum–Saunders (BS) distribution was originally proposed as a failure time distribution for fatigue failure caused under cyclic loading. BS model is a positively skewed statistical distribution which has received great attention in recent decades. Several extensions of this distribution with various degrees of skewness, kurtosis and modality are considered. In particular, a generalized version of this model was derived based on symmetrical distributions in the real line named the generalized BS (GBS) distribution. In this article, we propose a new family of life distributions, generated from elliptically contoured distributions, and the density and some of its properties are obtained. Explicit expressions for the density of a number of specific elliptical distributions, such as Pearson type VII, t, Cauchy, Kotz type, normal, Laplace and logistic are found. Another generalization of the BS distribution is also presented using skew-elliptical distribution which makes its symmetry more flexible. Finally, some examples are provided to illustrate application of the distribution.