发表机构
University of Brasilia; Federal University of Campina Grande（巴西利亚大学; 坎皮纳格兰德联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于GAMLSS框架的广义Birnbaum-Saunders回归模型，将协变量效应纳入所有三个参数，其中一参数直接解释为中位数，采用最大似然估计和Wald检验，模拟和实际应用验证了其灵活性和有效性。
AI 中文摘要
Birnbaum-Saunders（BS）分布已成为广泛用于正偏态连续数据的模型。已有多种BS分布的扩展被提出，包括将其参数与协变量关联的回归公式。在本文中，我们为广义Birnbaum-Saunders（GBS）分布引入了一种新的回归模型，该扩展在文献中受到的关注有限，尽管它提供了更强的物理解释。所提出的框架遵循位置、尺度和形状广义可加模型（GAMLSS）的结构，允许将协变量效应纳入分布的所有三个参数，从而为数据建模提供更大的灵活性。特别地，其中一个模型参数直接解释为响应变量的中位数，便于解释协变量对条件中位数的影响。参数估计通过最大似然进行，并基于Wald检验提出假设检验。所提出的回归模型通过R中的gamlss包实现，允许访问广泛的模型拟合、诊断和评估工具。进行了蒙特卡洛模拟研究，以调查最大似然估计量的有限样本性能。结果表明，估计量表现出理想的特性，随着样本量的增加，偏差减小且效率提高。此外，研究了Wald检验的行为，显示在中等至大样本量下具有良好的性能。最后，两个实际数据应用说明了所提出的GBS回归模型的实际有用性，证明其相对于BS模型是建模正偏态数据的灵活替代方案。
英文摘要
The Birnbaum-Saunders (BS) distribution has become a widely used model for positive and asymmetric continuous data. Several extensions of the BS distribution have been proposed, including regression formulations that relate its parameters to covariates. In this paper, we introduce a new regression model for the Generalized Birnbaum-Saunders (GBS) distribution, an extension that has received limited attention in the literature despite offering a stronger physical interpretation. The proposed framework follows the structure of Generalized Additive Models for Location, Scale, and Shape (GAMLSS), allowing covariate effects to be incorporated into all three parameters of the distribution, thereby providing greater flexibility for modeling data. In particular, one of the model parameters has a direct interpretation as the median of the response variable, facilitating the interpretation of covariate effects on the conditional median. Parameter estimation is performed via maximum likelihood, and hypothesis tests are proposed based on the Wald test. The proposed regression model is implemented in R through the gamlss package, allowing access to a broad range of tools for model fitting, diagnostics, and assessment. Monte Carlo simulation studies are conducted to investigate the finite-sample performance of the maximum likelihood estimators. The results show that the estimators exhibit desirable properties, with bias decreasing and efficiency increasing as sample size grows. Additionally, the behavior of the Wald test is investigated, showing good performance for moderate to large sample sizes. Finally, two applications to real data illustrate the practical usefulness of the proposed GBS regression model, demonstrating that it is a flexible alternative for modeling positive and asymmetric data compared to the BS model
