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An extended Birnbaum–Saunders distribution: Theory, estimation, and applications

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  • Gauss M. Cordeiro
  • Maria Do Carmo S. Lima
  • Audrey H.M.A. Cysneiros
  • Marcelino A. R. Pascoa
  • Rodrigo R. Pescim
  • Edwin M. M. Ortega

Abstract

Birnbaum and Saunders (1969a) pioneered a lifetime model which is commonly used in reliability studies. Based on this distribution, a new model called the gamma Birnbaum–Saunders distribution is proposed for describing fatigue life data. Several properties of the new distribution including explicit expressions for the ordinary and incomplete moments, generating and quantile functions, mean deviations, density function of the order statistics, and their moments are derived. We discuss the method of maximum likelihood and a Bayesian approach to estimate the model parameters. The superiority of the new model is illustrated by means of three failure real data sets. We also propose a new extended regression model based on the logarithm of the new distribution. The last model can be very useful to the analysis of real data and provide more realistic fits than other special regression models.

Suggested Citation

  • Gauss M. Cordeiro & Maria Do Carmo S. Lima & Audrey H.M.A. Cysneiros & Marcelino A. R. Pascoa & Rodrigo R. Pescim & Edwin M. M. Ortega, 2016. "An extended Birnbaum–Saunders distribution: Theory, estimation, and applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(8), pages 2268-2297, April.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:8:p:2268-2297
    DOI: 10.1080/03610926.2013.879182
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    Cited by:

    1. Guillermo Martínez-Flórez & Roger Tovar-Falón & Héctor W. Gómez, 2024. "Mathematical Formalization and Applications to Data with Excess of Zeros and Ones of the Unit-Proportional Hazard Inflated Models," Mathematics, MDPI, vol. 12(22), pages 1-23, November.
    2. Guillermo Martínez-Flórez & Roger Tovar-Falón & Carlos Barrera-Causil, 2024. "Dichotomous Proportional Hazard Regression Model: A Case Study on Students’ Dropout," Mathematics, MDPI, vol. 12(14), pages 1-14, July.

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