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Bayesian analysis of Birnbaum-Saunders distribution with partial information

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  • Xu, Ancha
  • Tang, Yincai

Abstract

In Bayesian analysis with objective priors, it should be justified that the posterior distribution is proper. In this paper, we show that the reference prior (or independent Jeffreys prior) of a two-parameter Birnbaum-Saunders distribution will result in an improper posterior distribution. However, the posterior distributions are proper based on the reference priors with partial information (RPPI). Based on censored samples, slice sampling is utilized to obtain the Bayesian estimators based on RPPI. Monte Carlo simulations are used to compare the efficiencies of different RPPIs, to assess the sensitivity of the choice of the priors, and to compare the Bayesian estimators with the maximum likelihood estimators, for various scales of sample size and degree of censoring. A real data set is analyzed for illustrative purpose.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:7:p:2324-2333
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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. 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.
    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. Xu, Ancha & Tang, Yincai, 2010. "Reference analysis for Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 185-192, January.
    5. 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.
    6. 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.
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    Citations

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    Cited by:

    1. Kalanka P. Jayalath, 2024. "Improved Bayesian Inferences for Right-Censored Birnbaum–Saunders Data," Mathematics, MDPI, vol. 12(6), pages 1-14, March.
    2. 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.
    3. 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.
    4. 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.
    5. Naijun Sha, 2018. "Statistical Inference for Progressive Stress Accelerated Life Testing with Birnbaum-Saunders Distribution," Stats, MDPI, vol. 1(1), pages 1-15, December.
    6. Filidor Vilca & Caio L. N. Azevedo & N. Balakrishnan, 2017. "Bayesian inference for sinh-normal/independent nonlinear regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(11), pages 2052-2074, August.
    7. Fernández, Arturo J., 2013. "Smallest Pareto confidence regions and applications," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 11-25.
    8. Mahdi Teimouri, 2023. "Fast Bayesian Inference for Birnbaum-Saunders Distribution," Computational Statistics, Springer, vol. 38(2), pages 569-601, June.

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