Arrué Jaime, Arellano-Valle Reinaldo B, Gómez Héctor W, Leiva Víctor
Department of Mathematics, Universidad de Antofagasta, Antofagasta, Chile.
Department of Statistics, Pontificia Universidad Católica de Chile, Santiago, Chile.
J Appl Stat. 2019 Oct 3;47(13-15):2690-2710. doi: 10.1080/02664763.2019.1668365. eCollection 2020.
The Birnbaum-Saunders distribution is a widely studied model with diverse applications. Its origins are in the modeling of lifetimes associated with material fatigue. By using a motivating example, we show that, even when lifetime data related to fatigue are modeled, the Birnbaum-Saunders distribution can be unsuitable to fit these data in the distribution tails. Based on the nice properties of the Birnbaum-Saunders model, in this work, we use a modified skew-normal distribution to construct such a model. This allows us to obtain flexibility in skewness and kurtosis, which is controlled by a shape parameter. We provide a mathematical characterization of this new type of Birnbaum-Saunders distribution and then its statistical characterization is derived by using the maximum-likelihood method, including the associated information matrices. In order to improve the inferential performance, we correct the bias of the corresponding estimators, which is supported by a simulation study. To conclude our investigation, we retake the motivating example based on fatigue life data to show the good agreement between the new type of Birnbaum-Saunders distribution proposed in this work and the data, reporting its potential applications.
Birnbaum-Saunders分布是一个得到广泛研究且应用多样的模型。它起源于与材料疲劳相关的寿命建模。通过一个启发性的例子，我们表明，即使在对与疲劳相关的寿命数据进行建模时，Birnbaum-Saunders分布在分布尾部可能并不适合拟合这些数据。基于Birnbaum-Saunders模型的良好性质，在这项工作中，我们使用一种修正的偏态正态分布来构建这样一个模型。这使我们能够在偏度和峰度上获得灵活性，其由一个形状参数控制。我们给出了这种新型Birnbaum-Saunders分布的数学特征，然后通过最大似然法推导其统计特征，包括相关的信息矩阵。为了提高推断性能，我们校正了相应估计量的偏差，这得到了一项模拟研究的支持。为了结束我们的研究，我们重新采用基于疲劳寿命数据的启发性例子，以展示这项工作中提出的新型Birnbaum-Saunders分布与数据之间的良好一致性，并报告其潜在应用。
