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Characterization of Differentiable Copulas

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  • Saikat Mukherjee
  • Farhad Jafari
  • Jong-Min Kim

Abstract

This paper proposes a new class of copulas which characterize the set of all twice continuously differentiable copulas. We show that our proposed new class of copulas is a new generalized copula family that include not only asymmetric copulas but also all smooth copula families available in the current literature. Spearman's rho and Kendall's tau for our new Fourier copulas which are asymmetric are introduced. Furthermore, an approximation method is discussed in order to optimize Spearman's rho and the corresponding Kendall's tau.

Suggested Citation

  • Saikat Mukherjee & Farhad Jafari & Jong-Min Kim, 2012. "Characterization of Differentiable Copulas," Papers 1210.2953, arXiv.org.
    • Handle: RePEc:arx:papers:1210.2953
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    References listed on IDEAS

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    1. Liebscher, Eckhard, 2008. "Construction of asymmetric multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2234-2250, November.
    2. Cécile Amblard & Stéphane Girard, 2009. "A new extension of bivariate FGM copulas," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 1-17, June.
    3. Rodríguez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2004. "A new class of bivariate copulas," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 315-325, February.
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