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On bivariate Kumaraswamy-distorted copulas

Author

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  • Ranadeera Gamage Madhuka Samanthi
  • Jungsywan Sepanski

Abstract

We propose families of bivariate copulas based on the Kumaraswamy distortion of existing copulas. With the additional two parameters in the Kumaraswamy distribution, the induced copulas permit more flexibility in tail behaviors. The framework employed in this paper also provides a method for generating new Archimedean copula models. Two theorems linking the original tail dependence behaviors and those of the distorted copula are derived for distortions that are asymptotically proportional to the power transformation in the lower tail and to the dual-power transformation in the upper tail. We also derive explicit formulas for the Kendall’s τ coefficients, tail order parameters and tail order functions for the induced copulas when Gumbel, Clayton, Frank and Galambos are distorted. An empirical application is also presented.

Suggested Citation

  • Ranadeera Gamage Madhuka Samanthi & Jungsywan Sepanski, 2022. "On bivariate Kumaraswamy-distorted copulas," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(8), pages 2477-2495, April.
  • Handle: RePEc:taf:lstaxx:v:51:y:2022:i:8:p:2477-2495
    DOI: 10.1080/03610926.2020.1777303
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    Cited by:

    1. Aisha Fayomi & Ehab M. Almetwally & Maha E. Qura, 2023. "Exploring New Horizons: Advancing Data Analysis in Kidney Patient Infection Rates and UEFA Champions League Scores Using Bivariate Kavya–Manoharan Transformation Family of Distributions," Mathematics, MDPI, vol. 11(13), pages 1-37, July.

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