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The [beta]-Birnbaum-Saunders distribution: An improved distribution for fatigue life modeling

Author

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  • Cordeiro, Gauss M.
  • Lemonte, Artur J.

Abstract

Birnbaum and Saunders (1969a) introduced a probability distribution which is commonly used in reliability studies. For the first time, based on this distribution, the so-called [beta]-Birnbaum-Saunders distribution is proposed for fatigue life modeling. Various properties of the new model including expansions for the moments, moment generating function, mean deviations, density function of the order statistics and their moments are derived. We discuss maximum likelihood estimation of the model's parameters. The superiority of the new model is illustrated by means of three failure real data sets.

Suggested Citation

  • Cordeiro, Gauss M. & Lemonte, Artur J., 2011. "The [beta]-Birnbaum-Saunders distribution: An improved distribution for fatigue life modeling," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1445-1461, March.
  • Handle: RePEc:eee:csdana:v:55:y:2011:i:3:p:1445-1461
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    References listed on IDEAS

    as
    1. Lemonte, Artur J. & Cribari-Neto, Francisco & Vasconcellos, Klaus L.P., 2007. "Improved statistical inference for the two-parameter Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4656-4681, May.
    2. Meintanis, Simos G., 2010. "Inference procedures for the Birnbaum-Saunders distribution and its generalizations," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 367-373, February.
    3. Wu, Jianrong & Wong, A. C. M., 2004. "Improved interval estimation for the two-parameter Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 47(4), pages 809-821, November.
    4. Kundu, Debasis & Kannan, Nandini & Balakrishnan, N., 2008. "On the hazard function of Birnbaum-Saunders distribution and associated inference," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2692-2702, January.
    5. Pescim, Rodrigo R. & Demétrio, Clarice G.B. & Cordeiro, Gauss M. & Ortega, Edwin M.M. & Urbano, Mariana R., 2010. "The beta generalized half-normal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 945-957, April.
    6. repec:eee:reensy:v:91:y:2006:i:6:p:689-697 is not listed on IDEAS
    7. Yousry Abdelkader, 2004. "Computing the moments of order statistics from nonidentically distributed Erlang variables," Statistical Papers, Springer, vol. 45(4), pages 563-570, October.
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    Cited by:

    1. Vilca, Filidor & Balakrishnan, N. & Zeller, Camila Borelli, 2014. "The bivariate Sinh-Elliptical distribution with applications to Birnbaum–Saunders distribution and associated regression and measurement error models," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 1-16.
    2. repec:eee:csdana:v:56:y:2012:i:12:p:3887-3897 is not listed on IDEAS

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