Skew-normal/independent distributions provide an attractive class of asymmetric heavy-tailed distributions to the usual symmetric normal distribution. We use this class of distributions here to derive a robust generalization of sinh-normal distributions (Rieck in Statistical analysis for the Birnbaum–Saunders fatigue life distribution, 1989), we then propose robust nonlinear regression models, generalizing the Birnbaum–Saunders regression models proposed by Rieck and Nedelman (Technometrics 33:51–60, 1991) that have been studied extensively. The proposed regression models have a nice hierarchical representation that facilitates easy implementation of an EM algorithm for the maximum likelihood estimation of model parameters and provide a robust alternative to estimation of parameters. Simulation studies as well as applications to a real dataset are presented to illustrate the usefulness of the proposed model as well as all the inferential methods developed here.

偏正态/独立分布提供了比通常的对称正态分布更有吸引力的不对称重尾分布。我们在这里使用此类分布来推导正态分布的鲁棒概括（Rieck在Birnbaum–Saunders疲劳寿命分布的统计分析中，1989），然后我们提出了鲁棒的非线性回归模型，对Birnbaum–Saunders回归模型进行了概括由Rieck和Nedelman（Technometrics 33：51–60，1991）进行了广泛的研究。所提出的回归模型具有很好的层次结构表示形式，可简化模型参数的最大似然估计的EM算法的轻松实现，并为参数估计提供可靠的替代方法。