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

Author

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  • Jaime Arrué
  • Reinaldo B. Arellano-Valle
  • Héctor W. Gómez
  • Víctor Leiva

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.

Suggested Citation

  • Jaime Arrué & Reinaldo B. Arellano-Valle & Héctor W. Gómez & Víctor Leiva, 2020. "On a new type of Birnbaum-Saunders models and its inference and application to fatigue data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(13-15), pages 2690-2710, November.
    • Handle: RePEc:taf:japsta:v:47:y:2020:i:13-15:p:2690-2710
    DOI: 10.1080/02664763.2019.1668365
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