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A note on distortion effects on the strength of bivariate copula tail dependence

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  • Sepanski, Jungsywan H.

Abstract

This note presents relationships between a base copula and the copula induced by distortion of the base copula in the strength of tail dependence measured by tail dependence coefficients and tail orders. We derive a theorem that determines the relationships for distortion functions satisfying conditions related to regular variation. In addition to the well-known logarithmic, power and dual-power distortions, Lomax-distribution and Weibull-distribution based distortions are considered. The results can be readily applied to distortions constructed by compositions of the considered distortions.

Suggested Citation

  • Sepanski, Jungsywan H., 2020. "A note on distortion effects on the strength of bivariate copula tail dependence," Statistics & Probability Letters, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:stapro:v:166:y:2020:i:c:s0167715220301978
    DOI: 10.1016/j.spl.2020.108894
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    References listed on IDEAS

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    1. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    2. 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.
    3. 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.
    4. Hua, Lei & Joe, Harry, 2011. "Tail order and intermediate tail dependence of multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1454-1471, November.
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    Cited by:

    1. Hu, Shuang & Peng, Zuoxiang & Nadarajah, Saralees, 2022. "Tail dependence functions of the bivariate Hüsler–Reiss model," Statistics & Probability Letters, Elsevier, vol. 180(C).
    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.

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