IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v52y2008i11p4939-4950.html
   My bibliography  Save this article

On Birnbaum-Saunders inference

Author

Listed:
  • Cysneiros, Audrey H.M.A.
  • Cribari-Neto, Francisco
  • Araújo Jr., Carlos A.G.

Abstract

The Birnbaum-Saunders distribution, also known as the fatigue-life distribution, is frequently used in reliability studies. We obtain adjustments to the Birnbaum-Saunders profile likelihood function. The modified versions of the likelihood function were obtained for both the shape and scale parameters, i.e., we take the shape parameter to be of interest and the scale parameter to be of nuisance, and then consider the situation in which the interest lies in performing inference on the scale parameter with the shape parameter entering the modeling in nuisance fashion. Modified profile maximum likelihood estimators are obtained by maximizing the corresponding adjusted likelihood functions. We present numerical evidence on the finite sample behavior of the different estimators and associated likelihood ratio tests. The results favor the adjusted estimators and tests we propose. A novel aspect of the profile likelihood adjustments obtained in this paper is that they yield improved point estimators and tests. The two profile likelihood adjustments work well when inference is made on the shape parameter, and one of them displays superior behavior when it comes to performing hypothesis testing inference on the scale parameter. Two empirical applications are briefly presented.

Suggested Citation

  • Cysneiros, Audrey H.M.A. & Cribari-Neto, Francisco & Araújo Jr., Carlos A.G., 2008. "On Birnbaum-Saunders inference," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4939-4950, July.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:11:p:4939-4950
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(08)00206-5
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    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. 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. Steven E. Stern, 1997. "A Second‐order Adjustment to the Profile Likelihood in the Case of a Multidimensional Parameter of Interest," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(3), pages 653-665.
    3. 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.
    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. Bhatti, Chad R., 2010. "The Birnbaum–Saunders autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2062-2078.
    2. Fonseca, Rodney V. & Cribari-Neto, Francisco, 2018. "Inference in a bimodal Birnbaum–Saunders model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 134-159.
    3. Barreto, Larissa Santana & Cysneiros, Audrey H.M.A. & Cribari-Neto, Francisco, 2013. "Improved Birnbaum–Saunders inference under type II censoring," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 68-81.
    4. Azevedo, Cecilia & Leiva, Víctor & Athayde, Emilia & Balakrishnan, N., 2012. "Shape and change point analyses of the Birnbaum–Saunders-t hazard rate and associated estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3887-3897.

    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. 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.
    2. 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.
    3. Wang, Bing Xing, 2012. "Generalized interval estimation for the Birnbaum–Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4320-4326.
    4. Barreto, Larissa Santana & Cysneiros, Audrey H.M.A. & Cribari-Neto, Francisco, 2013. "Improved Birnbaum–Saunders inference under type II censoring," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 68-81.
    5. 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.
    6. 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.
    7. Naijun Sha, 2018. "Statistical Inference for Progressive Stress Accelerated Life Testing with Birnbaum-Saunders Distribution," Stats, MDPI, vol. 1(1), pages 1-15, December.
    8. 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.
    9. Mahdi Teimouri, 2023. "Fast Bayesian Inference for Birnbaum-Saunders Distribution," Computational Statistics, Springer, vol. 38(2), pages 569-601, June.
    10. Fonseca, Rodney V. & Cribari-Neto, Francisco, 2018. "Inference in a bimodal Birnbaum–Saunders model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 134-159.
    11. Li, Ai-Ping & Xie, Feng-Chang, 2012. "Diagnostics for a class of survival regression models with heavy-tailed errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4204-4214.
    12. Naijun Sha, 2019. "A New Inference Approach for Type-II Generalized Birnbaum-Saunders Distribution," Stats, MDPI, vol. 2(1), pages 1-16, February.
    13. 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.
    14. Xu, Ancha & Tang, Yincai, 2010. "Reference analysis for Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 185-192, January.
    15. Kakizawa, Yoshihide, 2017. "Third-order average local powers of Bartlett-type adjusted tests: Ordinary versus adjusted profile likelihood," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 98-120.
    16. Bhatti, Chad R., 2010. "The Birnbaum–Saunders autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2062-2078.
    17. Barros, Michelli & Paula, Gilberto A. & Leiva, Víctor, 2009. "An R implementation for generalized Birnbaum-Saunders distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1511-1528, February.
    18. 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.
    19. 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.
    20. Mahdi Teimouri, 2022. "bccp: an R package for life-testing and survival analysis," Computational Statistics, Springer, vol. 37(1), pages 469-489, March.

    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:eee:csdana:v:52:y:2008:i:11:p:4939-4950. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.