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.

中文翻译：

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【特邀教程】伯恩鲍姆-桑德斯回归模型：三种方法的对比评价

本研究调查了基于 Birnbaum-Saunders 分布的三个回归模型。第一个模型直接通过 Birnbaum-Saunders 分布获得；第二个模型是通过响应变量的对数变换获得的；第三个模型采用该分布的平均参数化。本研究的主要目的是比较三个 Birnbaum-Saunders 回归模型的性能。第二个目标是在分析遵循 Birnbaum-Saunders 分布的数据时提供一种工具来选择最佳回归模型。通过使用 Monte Carlo 模拟和 R 软件，我们评估了相应估计量以及 Cox-Snell 和随机分位数残差的行为。提供了带有真实数据的插图以比较所研究的回归模型。