IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v55y2011i7p2388-2399.html
   My bibliography  Save this article

Testing hypotheses in the Birnbaum-Saunders distribution under type-II censored samples

Author

Listed:
  • Lemonte, Artur J.
  • Ferrari, Silvia L.P.

Abstract

The two-parameter Birnbaum-Saunders distribution has been used successfully to model fatigue failure times. Although censoring is typical in reliability and survival studies, little work has been published on the analysis of censored data for this distribution. In this paper, we address the issue of performing testing inference on the two parameters of the Birnbaum-Saunders distribution under type-II right censored samples. The likelihood ratio statistic and a recently proposed statistic, the gradient statistic, provide a convenient framework for statistical inference in such a case, since they do not require to obtain, estimate or invert an information matrix, which is an advantage in problems involving censored data. An extensive Monte Carlo simulation study is carried out in order to investigate and compare the finite sample performance of the likelihood ratio and the gradient tests. Our numerical results show evidence that the gradient test should be preferred. Further, we also consider the generalized Birnbaum-Saunders distribution under type-II right censored samples and present some Monte Carlo simulations for testing the parameters in this class of models using the likelihood ratio and gradient tests. Three empirical applications are presented.

Suggested Citation

  • Lemonte, Artur J. & Ferrari, Silvia L.P., 2011. "Testing hypotheses in the Birnbaum-Saunders distribution under type-II censored samples," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2388-2399, July.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:7:p:2388-2399
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(11)00050-8
    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. 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. Kundu, Debasis & Joarder, Avijit, 2006. "Analysis of Type-II progressively hybrid censored data," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2509-2528, June.
    4. Lemonte, Artur J. & Ferrari, Silvia L.P., 2011. "Size and power properties of some tests in the Birnbaum-Saunders regression model," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1109-1117, February.
    5. 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.
    6. Wu, Jianrong & Wong, A. C. M., 2004. "Improved interval estimation for the two-parameter Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 47(4), pages 809-821, November.
    7. Xu, Ancha & Tang, Yincai, 2010. "Reference analysis for Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 185-192, January.
    8. Bhatti, Chad R., 2010. "The Birnbaum–Saunders autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2062-2078.
    9. 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.
    10. 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.
    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. 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.
    2. Zhu, Xiaojun & Balakrishnan, N., 2015. "Birnbaum–Saunders distribution based on Laplace kernel and some properties and inferential issues," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 1-10.
    3. Fernández, Arturo J. & Pérez-González, Carlos J., 2012. "Optimal acceptance sampling plans for log-location–scale lifetime models using average risks," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 719-731.
    4. Fernández, Arturo J., 2013. "Smallest Pareto confidence regions and applications," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 11-25.
    5. Lemonte, Artur J., 2013. "On the gradient statistic under model misspecification," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 390-398.

    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. Wang, Bing Xing, 2012. "Generalized interval estimation for the Birnbaum–Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4320-4326.
    2. Lemonte, Artur J. & Ferrari, Silvia L.P., 2011. "Size and power properties of some tests in the Birnbaum-Saunders regression model," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1109-1117, February.
    3. 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.
    4. Mahdi Teimouri, 2023. "Fast Bayesian Inference for Birnbaum-Saunders Distribution," Computational Statistics, Springer, vol. 38(2), pages 569-601, June.
    5. 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.
    6. 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.
    7. 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.
    8. Lemonte, Artur J., 2013. "A new extended Birnbaum–Saunders regression model for lifetime modeling," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 34-50.
    9. 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.
    10. Cordeiro, Gauss M. & Lemonte, Artur J., 2011. "The [beta]-Birnbaum-Saunders distribution: An improved distribution for fatigue life modeling," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1445-1461, March.
    11. Kalanka P. Jayalath, 2024. "Improved Bayesian Inferences for Right-Censored Birnbaum–Saunders Data," Mathematics, MDPI, vol. 12(6), pages 1-14, March.
    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. Bhatti, Chad R., 2010. "The Birnbaum–Saunders autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2062-2078.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.

    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:55:y:2011:i:7:p:2388-2399. 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.