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

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

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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.

Original languageEnglish
Pages (from-to)2690-2710
Number of pages21
JournalJournal of Applied Statistics
Issue number13-15
StatePublished - 17 Nov 2020


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


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