IDEAS home Printed from https://ideas.repec.org/a/spr/jstada/v7y2020i1d10.1186_s40488-020-00110-z.html
   My bibliography  Save this article

New families of bivariate copulas via unit weibull distortion

Author

Listed:
  • Fadal A.A. Aldhufairi

    (Central Michigan University)

  • Jungsywan H. Sepanski

    (Central Michigan University)

Abstract

This paper introduces a new family of bivariate copulas constructed using a unit Weibull distortion. Existing copulas play the role of the base or initial copulas that are transformed or distorted into a new family of copulas with additional parameters, allowing more flexibility and better fit to data. We present a general form for the new bivariate copula function and its conditional and density distributions. The tail behaviors are investigated and indicate the unit Weibull distortion may result in new copulas with upper tail dependence when the base copula has no upper tail dependence. The concordance ordering and Kendall’s tau are derived for the cases when the base copulas are Archimedean, such as the Clayton and Frank copulas. The Loss-ALEA data are analyzed to evaluate the performance of the proposed new families of copulas.

Suggested Citation

  • Fadal A.A. Aldhufairi & Jungsywan H. Sepanski, 2020. "New families of bivariate copulas via unit weibull distortion," Journal of Statistical Distributions and Applications, Springer, vol. 7(1), pages 1-20, December.
    • Handle: RePEc:spr:jstada:v:7:y:2020:i:1:d:10.1186_s40488-020-00110-z
    DOI: 10.1186/s40488-020-00110-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1186/s40488-020-00110-z
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1186/s40488-020-00110-z?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
    ---><---

    References listed on IDEAS

    as
    1. Christian Genest & Kilani Ghoudi & Louis-Paul Rivest, 1998. "“Understanding Relationships Using Copulas,” by Edward Frees and Emiliano Valdez, January 1998," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(3), pages 143-149.
    2. Di Bernardino Elena & Rullière Didier, 2013. "On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators," Dependence Modeling, De Gruyter, vol. 1, pages 1-36, October.
    3. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    4. Kahadawala Cooray, 2019. "A new extension of the FGM copula for negative association," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(8), pages 1902-1919, April.
    5. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    6. Edward Frees, 2018. "Loss Data Analytics," Papers 1808.06718, arXiv.org.
    7. repec:hal:wpaper:hal-00834000 is not listed on IDEAS
    8. Patricia Mariela Morillas, 2005. "A method to obtain new copulas from a given one," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(2), pages 169-184, April.
    9. Ranadeera G. M. Samanthi & Jungsywan Sepanski, 2019. "A bivariate extension of the beta generated distribution derived from copulas," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(5), pages 1043-1059, March.
    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. Jungsywan H. Sepanski & Xiwen Wang, 2023. "New Classes of Distortion Risk Measures and Their Estimation," Risks, MDPI, vol. 11(11), pages 1-21, November.

    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. Elena Di Bernardino & Didier Rullière, 2016. "On tail dependence coefficients of transformed multivariate Archimedean copulas," Post-Print hal-00992707, HAL.
    2. Fadal Abdullah-A Aldhufairi & Ranadeera G.M. Samanthi & Jungsywan H. Sepanski, 2020. "New Families of Bivariate Copulas via Unit Lomax Distortion," Risks, MDPI, vol. 8(4), pages 1-19, October.
    3. Genest, Christian & Masiello, Esterina & Tribouley, Karine, 2009. "Estimating copula densities through wavelets," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 170-181, April.
    4. Di Bernardino Elena & Rullière Didier, 2013. "On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators," Dependence Modeling, De Gruyter, vol. 1, pages 1-36, October.
    5. Amjad, Muhammad & Akbar, Muhammad & Ullah, Hamd, 2022. "A copula-based approach for creating an index of micronutrient intakes at household level in Pakistan," Economics & Human Biology, Elsevier, vol. 46(C).
    6. Mohamed Achibi & Michel Broniatowski & Catherine Duveau & Alice Marboeuf, 2012. "Bivariate Cox models and copulas," Journal of Risk and Reliability, , vol. 226(5), pages 476-487, October.
    7. Di Bernardino Elena & Rullière Didier, 2016. "On an asymmetric extension of multivariate Archimedean copulas based on quadratic form," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-20, December.
    8. Elena Di Bernardino & Didier Rullière, 2016. "A note on upper-patched generators for Archimedean copulas," Working Papers hal-01347869, HAL.
    9. Hobæk Haff, Ingrid, 2012. "Comparison of estimators for pair-copula constructions," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 91-105.
    10. Hofert, Marius & Mächler, Martin & McNeil, Alexander J., 2012. "Likelihood inference for Archimedean copulas in high dimensions under known margins," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 133-150.
    11. Girard Stéphane, 2018. "Transformation Of A Copula Using The Associated Co-Copula," Dependence Modeling, De Gruyter, vol. 6(1), pages 298-308, December.
    12. Jean-David Fermanian, 2012. "An overview of the goodness-of-fit test problem for copulas," Papers 1211.4416, arXiv.org.
    13. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
    14. Zhang, Shulin & Okhrin, Ostap & Zhou, Qian M. & Song, Peter X.-K., 2016. "Goodness-of-fit test for specification of semiparametric copula dependence models," Journal of Econometrics, Elsevier, vol. 193(1), pages 215-233.
    15. Emura, Takeshi & Lin, Chien-Wei & Wang, Weijing, 2010. "A goodness-of-fit test for Archimedean copula models in the presence of right censoring," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3033-3043, December.
    16. Durante Fabrizio & Puccetti Giovanni & Scherer Matthias & Vanduffel Steven, 2016. "Stat Trek," Dependence Modeling, De Gruyter, vol. 4(1), pages 109-122, May.
    17. Miriam Jaser & Aleksey Min, 2021. "On tests for symmetry and radial symmetry of bivariate copulas towards testing for ellipticity," Computational Statistics, Springer, vol. 36(3), pages 1-26, September.
    18. Liang Zhu & Christine Lim & Wenjun Xie & Yuan Wu, 2017. "Analysis of tourism demand serial dependence structure for forecasting," Tourism Economics, , vol. 23(7), pages 1419-1436, November.

    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:jstada:v:7:y:2020:i:1:d:10.1186_s40488-020-00110-z. 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.