A study of exponential-type tails applied to Birnbaum-Saunders models

Chilean Statistical Society, 4(1) (2013), 91-101
http://chjs.soche.cl/papers/vol4n1_2013/ChJS-04-01-06.pdf

Birnbaum-Saunders distributions have increasingly been used in environmental sciences applications. A major concern is the adjustment of extreme quantiles. Environmental data have often tails in the Gumbel domain which corresponds to a null tail index and does not allow us to distinguish the different tail weights that might exist between distributions within this domain. Exponential-tail distributions form an important subgroup with the peculiarity of including a parameter that specifies the “penultimate” tail behavior. In particular, we analyze the penultimate tail behavior of Birnbaum- Saunders distributions. We find examples with“heavier” tails than the classical one that can better accommodate environmental data highly concentrated on the right tail. This is illustrated with an application.