On a new type of Birnbaum-Saunders models and its inference and application to fatigue data

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.

Keywords:

• Correction of bias
• fatigue life data
• maximum likelihood method
• Monte Carlo simulation
• R software
• skew-normal distribution

Acknowledgments

The authors would like to thank the editors and reviewers for their constructive comments on an earlier version of this manuscript which resulted in this improved version.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of J. Arrué and H.W. Gómez was supported by Grant SEMILLERO-UA-2019. The research of Víctor Leiva was supported partially by grant ‘Fondo Nacional de Desarrollo Científico y Tecnológico (Fondecyt) 1160868’ from the National Commission for Scientific and Technological.