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New Families of Bivariate Copulas via Unit Lomax Distortion

Author

Listed:
  • Fadal Abdullah-A Aldhufairi

    (Department of Statistics, Actuarial and Data Sciences, Central Michigan University, Mount Pleasant, MI 48859, USA)

  • Ranadeera G.M. Samanthi

    (Department of Statistics, Actuarial and Data Sciences, Central Michigan University, Mount Pleasant, MI 48859, USA)

  • Jungsywan H. Sepanski

    (Department of Statistics, Actuarial and Data Sciences, Central Michigan University, Mount Pleasant, MI 48859, USA)

Abstract

This article studies a new family of bivariate copulas constructed using the unit-Lomax distortion derived from a transformation of the non-negative Lomax random variable into a variable whose support is the unit interval. Existing copulas play the role of the base copulas that are distorted into new families of copulas with additional parameters, allowing more flexibility and better fit to data. We present general forms for the new bivariate copula function and its conditional and density distributions. The properties of the new family of the unit-Lomax induced copulas, including the tail behaviors, limiting cases in parameters, Kendall’s tau, and concordance order, are investigated for cases when the base copulas are Archimedean, such as the Clayton, Gumbel, and Frank copulas. An empirical application of the proposed copula model is presented. The unit-Lomax distorted copula models outperform the base copulas.

Suggested Citation

  • 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.
  • Handle: RePEc:gam:jrisks:v:8:y:2020:i:4:p:106-:d:427624
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    References listed on IDEAS

    as
    1. Lin, Feng & Peng, Liang & Xie, Jiehua & Yang, Jingping, 2018. "Stochastic distortion and its transformed copula," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 148-166.
    2. Nelsen, Roger B., 1997. "Dependence and Order in Families of Archimedean Copulas," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 111-122, January.
    3. Thu Thuy Nguyen & Van Chien Nguyen & Trong Nguyen Tran & David McMillan, 2020. "Oil price shocks against stock return of oil- and gas-related firms in the economic depression: A new evidence from a copula approach," Cogent Economics & Finance, Taylor & Francis Journals, vol. 8(1), pages 1799908-179, January.
    4. Nguyen, Thu Thuy & Tran, T.N. & Nguyen, V.C., 2020. "Oil price shocks against stock return of oil- and gas-related firms in the economic depression: A new evidence from a copula approach," OSF Preprints 4cm7b, Center for Open Science.
    5. 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.
    6. Yang, Xipei & Frees, Edward W. & Zhang, Zhengjun, 2011. "A generalized beta copula with applications in modeling multivariate long-tailed data," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 265-284, September.
    7. 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.
    8. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    9. Sepanski, Jungsywan H., 2020. "A note on distortion effects on the strength of bivariate copula tail dependence," Statistics & Probability Letters, Elsevier, vol. 166(C).
    10. Joe, Harry & Hu, Taizhong, 1996. "Multivariate Distributions from Mixtures of Max-Infinitely Divisible Distributions," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 240-265, May.
    11. repec:hal:wpaper:hal-00834000 is not listed on IDEAS
    12. 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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