On a new type of Birnbaum-Saunders models and its inference and application to fatigue data. Issue 13 (17th November 2020)

• Record Type: Journal Article
• Authors: Arrué, Jaime; Arellano-Valle, Reinaldo B.; Gómez, Héctor W.; Leiva, Víctor
• Is Part Of: Journal of applied statistics. Volume 47:Issue 13/15(2020)
• Page Start: 2690
• Page End: 2710
• Publication Date: 2020-11-17
• Subjects: Correction of bias -- fatigue life data -- maximum likelihood method -- Monte Carlo simulation -- R software -- skew-normal distribution; Statistics -- Periodicals; 519.5
• DOI: 10.1080/02664763.2019.1668365
• Languages: English
• ISSNs: 0266-4763

Abstract

ABSTRACT: 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.