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Bayesian analysis of Birnbaum–Saunders distribution via the generalized ratio-of-uniforms method

Author

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  • Min Wang

    (Michigan Technological University)

  • Xiaoqian Sun

    (Clemson University)

  • Chanseok Park

    (Pusan National University)

Abstract

This paper deals with the Bayesian inference for the parameters of the Birnbaum–Saunders distribution. We adopt the inverse-gamma priors for the shape and scale parameters because the continuous conjugate joint prior distribution does not exist and the reference prior (or independent Jeffreys’ prior) results in an improper posterior distribution. We propose an efficient sampling algorithm via the generalized ratio-of-uniforms method to compute the Bayesian estimates and the credible intervals. One appealing advantage of the proposed procedure over other sampling techniques is that it efficiently generates independent samples from the required posterior distribution. Simulation studies are conducted to investigate the behavior of the proposed method, and two real-data applications are analyzed for illustrative purposes.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:31:y:2016:i:1:d:10.1007_s00180-015-0629-z
    DOI: 10.1007/s00180-015-0629-z
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. Peter Neal & Gareth Roberts, 2008. "Optimal Scaling for Random Walk Metropolis on Spherically Constrained Target Densities," Methodology and Computing in Applied Probability, Springer, vol. 10(2), pages 277-297, June.
    5. Vilca, Filidor & Balakrishnan, N. & Zeller, Camila Borelli, 2014. "A robust extension of the bivariate Birnbaum–Saunders distribution and associated inference," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 418-435.
    6. Min Wang & Jing Zhao & Xiaoqian Sun & Chanseok Park, 2013. "Robust explicit estimation of the two-parameter Birnbaum--Saunders distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(10), pages 2259-2274, October.
    7. 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.
    8. Xu, Ancha & Tang, Yincai, 2010. "Reference analysis for Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 185-192, January.
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    Cited by:

    1. Kalanka P. Jayalath, 2021. "Fiducial Inference on the Right Censored Birnbaum–Saunders Data via Gibbs Sampler," Stats, MDPI, vol. 4(2), pages 1-15, May.
    2. Naijun Sha, 2018. "Statistical Inference for Progressive Stress Accelerated Life Testing with Birnbaum-Saunders Distribution," Stats, MDPI, vol. 1(1), pages 1-15, December.
    3. Mahdi Teimouri, 2023. "Fast Bayesian Inference for Birnbaum-Saunders Distribution," Computational Statistics, Springer, vol. 38(2), pages 569-601, June.
    4. Nanami Taketomi & Kazuki Yamamoto & Christophe Chesneau & Takeshi Emura, 2022. "Parametric Distributions for Survival and Reliability Analyses, a Review and Historical Sketch," Mathematics, MDPI, vol. 10(20), pages 1-23, October.
    5. Leiva, Víctor & Ruggeri, Fabrizio & Saulo, Helton & Vivanco, Juan F., 2017. "A methodology based on the Birnbaum–Saunders distribution for reliability analysis applied to nano-materials," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 192-201.

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