Flexible Log-Linear Birnbaum–Saunders Model

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Abstract
Rieck and Nedelman (1991) introduced the sinh-normal distribution. This model was built as a transformation of a N(0,1) distribution. In this paper, a generalization based on a flexible skew normal distribution is introduced. In this way, a more general model is obtained that can describe a range of asymmetric, unimodal and bimodal situations. The paper is divided into two parts. First, the properties of this new model, called flexible sinh-normal distribution, are obtained. In the second part, the flexible sinh-normal distribution is related to flexible Birnbaum–Saunders, introduced by Martínez-Flórez et al. (2019), to propose a log-linear model for lifetime data. Applications to real datasets are included to illustrate our findings.

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