[Invited tutorial] Birnbaum–Saunders regression models: a comparative evaluation of three approaches

This study investigates three regression models based on the Birnbaum–Saunders distribution. The first model is obtained directly through the Birnbaum–Saunders distribution; the second model is obtained via a logarithmic transformation in the response variable; and the third model employs a mean parametrization of this distribution. The primary objective of this study is to compare the performance of the three Birnbaum–Saunders regression models. The secondary objective is to provide a tool to choose the best model for regression when analysing data following a Birnbaum–Saunders distribution. By using Monte Carlo simulations and the R software, we evaluate the behaviour of the corresponding estimators, and of the Cox–Snell and randomized quantile residuals. An illustration with real data is provided to compare the investigated regression models.