A generalized Birnbaum-Saunders distribution with application to the air pollution data

Birnbaum-Saunders (BS) distribution is a model with positive domain thatis used in many fields including reliability and environmental studies. Thisarticle introduces a generalized version of the BS distribution which arisesfrom the shape mixture of skew normal distribution. A feasible EM typealgorithm is developed to obtain maximum likelihood (ML) estimates of pa-rameters of the new model. The asymptotic standard errors of ML estimatesare obtained via the information-based approximation. The robustness andapplication of the proposed methodology is illustrated through simulationstudies and air pollution analysis.

伯恩鲍姆-桑德斯（Birnbaum-Saunders, BS）分布是一类取值域为正的统计模型，已被广泛应用于可靠性工程、环境研究等多个领域。本文提出了BS分布的一种广义形式，该形式源于偏正态分布（skew normal distribution）的形状混合构造。针对该新模型，本文开发了一种可行的类EM算法以求解其参数的极大似然（ML）估计，并通过基于信息矩阵的近似方法得到了极大似然估计的渐近标准误。最后，通过仿真实验与空气污染数据分析，验证了所提方法的稳健性与实际应用价值。