In this paper, we introduce a new regression model for positive and skewed data, a log Birnbaum-Saunders model based on the centred skew-normal distribution, and we present a several inference tools for this model. Initially, we developed a new version of skew-sinh-normal distribution and we describe some of its properties. For the proposed regression model, we carry out, through of the expectation conditional maximization (ECM) algorithm, the parameter estimation, model fit assessment, model comparison and residual analysis. Finally, our model accommodates more suitably the asymmetry of the data, compared with the usual log Birnbaum-Saunders model, which is illustrated through real data analysis. keywords: Birnbaum-Saunders distribution; Skew normal distribution; Skew sinh-normal distribution; Frequentist inference; ECM algorithm.

中文翻译：

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中心参数化下基于偏态正态分布的对数 Birnbaum-Saunders 回归模型

在本文中，我们介绍了一种新的正态和偏态数据回归模型，一个基于中心偏态正态分布的 log Birnbaum-Saunders 模型，并为该模型提供了几种推理工具。最初，我们开发了一个新版本的 skew-sinh-normal 分布，并描述了它的一些特性。对于所提出的回归模型，我们通过期望条件最大化（ECM）算法进行了参数估计、模型拟合评估、模型比较和残差分析。最后，与通过实际数据分析说明的通常对数 Birnbaum-Saunders 模型相比，我们的模型更适合地适应数据的不对称性。关键词：伯恩鲍姆-桑德斯分布；偏态正态分布；偏斜正态分布；频率论推理；ECM 算法。