IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v80y2017i4d10.1007_s00184-017-0612-5.html
   My bibliography  Save this article

Estimation in generalized bivariate Birnbaum–Saunders models

Author

Listed:
  • Helton Saulo

    (Universidade Federal de Goiás
    McMaster University
    Universidade de Brasília)

  • N. Balakrishnan

    (McMaster University)

  • Xiaojun Zhu

    (McMaster University)

  • Jhon F. B. Gonzales

    (Universidad Nacional de San Agustín
    Universidad Continental)

  • Jeremias Leão

    (Universidade Federal do Amazonas)

Abstract

In this paper, we propose two moment-type estimation methods for the parameters of the generalized bivariate Birnbaum–Saunders distribution by taking advantage of some properties of the distribution. The proposed moment-type estimators are easy to compute and always exist uniquely. We derive the asymptotic distributions of these estimators and carry out a simulation study to evaluate the performance of all these estimators. The probability coverages of confidence intervals are also discussed. Finally, two examples are used to illustrate the proposed methods.

Suggested Citation

  • Helton Saulo & N. Balakrishnan & Xiaojun Zhu & Jhon F. B. Gonzales & Jeremias Leão, 2017. "Estimation in generalized bivariate Birnbaum–Saunders models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(4), pages 427-453, May.
    • Handle: RePEc:spr:metrik:v:80:y:2017:i:4:d:10.1007_s00184-017-0612-5
    DOI: 10.1007/s00184-017-0612-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-017-0612-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00184-017-0612-5?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. N. Balakrishnan & Xiaojun Zhu, 2015. "Inference for the bivariate Birnbaum–Saunders lifetime regression model and associated inference," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(7), pages 853-872, October.
    2. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    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. Naijun Sha, 2019. "A New Inference Approach for Type-II Generalized Birnbaum-Saunders Distribution," Stats, MDPI, vol. 2(1), pages 1-16, February.

    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. Kundu, Debasis & Balakrishnan, N. & Jamalizadeh, Ahad, 2013. "Generalized multivariate Birnbaum–Saunders distributions and related inferential issues," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 230-244.
    2. Falk, Michael, 1998. "A Note on the Comedian for Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 306-317, November.
    3. Kume, Alfred & Hashorva, Enkelejd, 2012. "Calculation of Bayes premium for conditional elliptical risks," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 632-635.
    4. Jacob, P. & Suquet, Ch., 1997. "Regression and asymptotical location of a multivariate sample," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 173-179, September.
    5. Tarpey, Thaddeus, 2000. "Parallel Principal Axes," Journal of Multivariate Analysis, Elsevier, vol. 75(2), pages 295-313, November.
    6. Isaac E. Cortés & Osvaldo Venegas & Héctor W. Gómez, 2022. "A Symmetric/Asymmetric Bimodal Extension Based on the Logistic Distribution: Properties, Simulation and Applications," Mathematics, MDPI, vol. 10(12), pages 1-17, June.
    7. Valdez, Emiliano A. & Chernih, Andrew, 2003. "Wang's capital allocation formula for elliptically contoured distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 517-532, December.
    8. Preinerstorfer, David & Pötscher, Benedikt M., 2017. "On The Power Of Invariant Tests For Hypotheses On A Covariance Matrix," Econometric Theory, Cambridge University Press, vol. 33(1), pages 1-68, February.
    9. Peng Ding, 2016. "On the Conditional Distribution of the Multivariate Distribution," The American Statistician, Taylor & Francis Journals, vol. 70(3), pages 293-295, July.
    10. Mittnik, Stefan, 2014. "VaR-implied tail-correlation matrices," Economics Letters, Elsevier, vol. 122(1), pages 69-73.
    11. Jonathan Raimana Chan & Thomas Huckle & Antoine Jacquier & Aitor Muguruza, 2021. "Portfolio optimisation with options," Papers 2111.12658, arXiv.org, revised Sep 2024.
    12. Lombardi, Marco J. & Veredas, David, 2009. "Indirect estimation of elliptical stable distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2309-2324, April.
    13. Fraiman, Ricardo & Moreno, Leonardo & Ransford, Thomas, 2023. "A Cramér–Wold theorem for elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    14. Arellano-Valle, Reinaldo B., 2001. "On some characterizations of spherical distributions," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 227-232, October.
    15. Villegas, Cristian & Paula, Gilberto A. & Cysneiros, Francisco José A. & Galea, Manuel, 2013. "Influence diagnostics in generalized symmetric linear models," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 161-170.
    16. Stöber, Jakob & Joe, Harry & Czado, Claudia, 2013. "Simplified pair copula constructions—Limitations and extensions," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 101-118.
    17. Jamalizadeh, A. & Balakrishnan, N., 2010. "Distributions of order statistics and linear combinations of order statistics from an elliptical distribution as mixtures of unified skew-elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1412-1427, July.
    18. Gómez, Héctor W. & Quintana, Fernando A. & Torres, Francisco J., 2007. "A new family of slash-distributions with elliptical contours," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 717-725, April.
    19. Santiago Pereda-Fernández, 2021. "Copula-Based Random Effects Models for Clustered Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 575-588, March.
    20. Battey, Heather & Linton, Oliver, 2014. "Nonparametric estimation of multivariate elliptic densities via finite mixture sieves," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 43-67.

    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:spr:metrik:v:80:y:2017:i:4:d:10.1007_s00184-017-0612-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.