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Fast Bayesian Inference for Birnbaum-Saunders Distribution

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  • Mahdi Teimouri

    (Gonbad Kavous University)

Abstract

In this work, we propose the Bayesian estimator for parameters of the Birnbaum-Saunders distribution based on conjugate, Jeffreys, and reference priors that can be implemented quite fast through Gibbs sampler. The Bayesian estimator based on conjugate prior for the Birnbaum-Saunders is new. Performance of the proposed Bayesian paradigm, based on three priors, is demonstrated by simulation and analyzing two sets of real data. Furthermore, it is shown through an extra real example that the Bayesian estimator can outperform the maximum likelihood estimator for the BS distribution when data are incomplete due to the progressive type-II censoring scheme. An R package called bibs has been uploaded to comprehensive R archive network (CRAN) at https://cran.r-project.org/web/packages/bibs/index.html for computing the Bayesian estimator, corresponding standard errors, and credible intervals.

Suggested Citation

  • Mahdi Teimouri, 2023. "Fast Bayesian Inference for Birnbaum-Saunders Distribution," Computational Statistics, Springer, vol. 38(2), pages 569-601, June.
    • Handle: RePEc:spr:compst:v:38:y:2023:i:2:d:10.1007_s00180-022-01234-3
    DOI: 10.1007/s00180-022-01234-3
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    References listed on IDEAS

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    1. Wang, Bing Xing, 2012. "Generalized interval estimation for the Birnbaum–Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4320-4326.
    2. Min Wang & Xiaoqian Sun & Chanseok Park, 2016. "Bayesian analysis of Birnbaum–Saunders distribution via the generalized ratio-of-uniforms method," Computational Statistics, Springer, vol. 31(1), pages 207-225, March.
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    4. Ng, H.K.T. & Kundu, D. & Balakrishnan, N., 2006. "Point and interval estimation for the two-parameter Birnbaum-Saunders distribution based on Type-II censored samples," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3222-3242, July.
    5. 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.
    6. Wang, Zhihui & Desmond, A.F. & Lu, Xuewen, 2006. "Modified censored moment estimation for the two-parameter Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 1033-1051, February.
    7. Kundu, Debasis & Balakrishnan, N. & Jamalizadeh, A., 2010. "Bivariate Birnbaum-Saunders distribution and associated inference," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 113-125, January.
    8. Ng, H. K. T. & Kundu, D. & Balakrishnan, N., 2003. "Modified moment estimation for the two-parameter Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 43(3), pages 283-298, July.
    9. Ortega, Edwin M.M. & Cordeiro, Gauss M. & Lemonte, Artur J., 2012. "A log-linear regression model for the β-Birnbaum–Saunders distribution with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 698-718.
    10. Achcar, Jorge Alberto, 1993. "Inferences for the Birnbaum-- Saunders fatigue life model using bayesian methods," Computational Statistics & Data Analysis, Elsevier, vol. 15(4), pages 367-380, May.
    11. Xu, Ancha & Tang, Yincai, 2011. "Bayesian analysis of Birnbaum-Saunders distribution with partial information," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2324-2333, July.
    12. Xu, Ancha & Tang, Yincai, 2010. "Reference analysis for Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 185-192, January.
    13. Manuel Galea & Victor Leiva-Sanchez & Gilberto Paula, 2004. "Influence Diagnostics in log-Birnbaum-Saunders Regression Models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(9), pages 1049-1064.
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