On a Birnbaum–Saunders distribution arising from a non-homogeneous Poisson process

The Birnbaum–Saunders distribution is based on the asymptotic normality of a sum of random variables. We propose a new version of this distribution assuming that the number of terms of such a sum depends on a non-homogeneous Poisson process. The classical Birnbaum–Saunders distribution is obtained when a homogeneous Poisson process is considered.