IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v40y2013i10p2259-2274.html
   My bibliography  Save this article

Robust explicit estimation of the two-parameter Birnbaum--Saunders distribution

Author

Listed:
  • Min Wang
  • Jing Zhao
  • Xiaoqian Sun
  • Chanseok Park

Abstract

The two-parameter Birnbaum--Saunders distribution is widely applicable to model failure times of fatiguing materials. Its maximum-likelihood estimators (MLEs) are very sensitive to outliers and also have no closed-form expressions. This motivates us to develop some alternative estimators. In this paper, we develop two robust estimators, which are also explicit functions of sample observations and are thus easy to compute. We derive their breakdown points and carry out extensive Monte Carlo simulation experiments to compare the performance of all the estimators under consideration. It has been observed from the simulation results that the proposed estimators outperform in a manner that is approximately comparable with the MLEs, whereas they are far superior in the presence of data contamination that often occurs in practical situations. A simple bias-reduction technique is presented to reduce the bias of the recommended estimators. Finally, the practical application of the developed procedures is illustrated with a real-data example.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:40:y:2013:i:10:p:2259-2274
    DOI: 10.1080/02664763.2013.809570
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2013.809570
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2013.809570?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Neil Marks, 2005. "Estimation of Weibull parameters from common percentiles," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(1), pages 17-24.
    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. 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.
    5. Xu, Ancha & Tang, Yincai, 2010. "Reference analysis for Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 185-192, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Camilo Lillo & Víctor Leiva & Orietta Nicolis & Robert G. Aykroyd, 2018. "L-moments of the Birnbaum–Saunders distribution and its extreme value version: estimation, goodness of fit and application to earthquake data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(2), pages 187-209, January.
    2. Xu Guo & Hecheng Wu & Gaorong Li & Qiuyue Li, 2017. "Inference for the common mean of several Birnbaum–Saunders populations," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(5), pages 941-954, April.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Kalanka P. Jayalath, 2024. "Improved Bayesian Inferences for Right-Censored Birnbaum–Saunders Data," Mathematics, MDPI, vol. 12(6), pages 1-14, March.
    3. Mahdi Teimouri, 2023. "Fast Bayesian Inference for Birnbaum-Saunders Distribution," Computational Statistics, Springer, vol. 38(2), pages 569-601, June.
    4. Wang, Bing Xing, 2012. "Generalized interval estimation for the Birnbaum–Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4320-4326.
    5. 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.
    6. 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.
    7. Leiva, Victor & Riquelme, Marco & Balakrishnan, N. & Sanhueza, Antonio, 2008. "Lifetime analysis based on the generalized Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2079-2097, January.
    8. 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.
    9. Naijun Sha, 2018. "Statistical Inference for Progressive Stress Accelerated Life Testing with Birnbaum-Saunders Distribution," Stats, MDPI, vol. 1(1), pages 1-15, December.
    10. 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.
    11. 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.
    12. Xie, Feng-Chang & Wei, Bo-Cheng, 2007. "Diagnostics analysis for log-Birnbaum-Saunders regression models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4692-4706, May.
    13. Xu, Ancha & Tang, Yincai, 2010. "Reference analysis for Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 185-192, January.
    14. 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.
    15. 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.
    16. Xiaojun Zhu & N. Balakrishnan & Helton Saulo, 2019. "On the existence and uniqueness of the maximum likelihood estimates of parameters of Laplace Birnbaum–Saunders distribution based on Type-I, Type-II and hybrid censored samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(7), pages 759-778, October.
    17. 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.
    18. Fang, Longxiang & Zhu, Xiaojun & Balakrishnan, N., 2016. "Stochastic comparisons of parallel and series systems with heterogeneous Birnbaum–Saunders components," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 131-136.
    19. Xiao, Qingchu & Liu, Zaiming & Balakrishnan, N. & Lu, Xuewen, 2010. "Estimation of the Birnbaum-Saunders regression model with current status data," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 326-332, February.
    20. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:japsta:v:40:y:2013:i:10:p:2259-2274. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.