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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
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    References listed on IDEAS

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    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(2013), 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.
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    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.

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