Open Access
May 2019 Failure rate of Birnbaum–Saunders distributions: Shape, change-point, estimation and robustness
Emilia Athayde, Assis Azevedo, Michelli Barros, Víctor Leiva
Braz. J. Probab. Stat. 33(2): 301-328 (May 2019). DOI: 10.1214/17-BJPS389


The Birnbaum–Saunders (BS) distribution has been largely studied and applied. A random variable with BS distribution is a transformation of another random variable with standard normal distribution. Generalized BS distributions are obtained when the normally distributed random variable is replaced by another symmetrically distributed random variable. This allows us to obtain a wide class of positively skewed models with lighter and heavier tails than the BS model. Its failure rate admits several shapes, including the unimodal case, with its change-point being able to be used for different purposes. For example, to establish the reduction in a dose, and then in the cost of the medical treatment. We analyze the failure rates of generalized BS distributions obtained by the logistic, normal and Student-t distributions, considering their shape and change-point, estimating them, evaluating their robustness, assessing their performance by simulations, and applying the results to real data from different areas.


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Emilia Athayde. Assis Azevedo. Michelli Barros. Víctor Leiva. "Failure rate of Birnbaum–Saunders distributions: Shape, change-point, estimation and robustness." Braz. J. Probab. Stat. 33 (2) 301 - 328, May 2019.


Received: 1 February 2016; Accepted: 1 November 2017; Published: May 2019
First available in Project Euclid: 4 March 2019

zbMATH: 07057449
MathSciNet: MR3919025
Digital Object Identifier: 10.1214/17-BJPS389

Keywords: Bootstrapping , likelihood-based methods , logistic , Monte Carlo simulation , normal and Student-t distributions , R computer language

Rights: Copyright © 2019 Brazilian Statistical Association

Vol.33 • No. 2 • May 2019
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