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Transformation of a copula using the associated co-copula

Author

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  • Girard Stéphane

    (Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, 38000Grenoble, France)

Abstract

We investigate the properties of a new transformation of copulas based on the co-copula and an univariate function. It is shown that several families in the copula literature can be interpreted as particular outputs of this transformation. Symmetry, association, ordering and dependence properties of the resulting copula are established.

Suggested Citation

  • Girard Stéphane, 2018. "Transformation of a copula using the associated co-copula," Dependence Modeling, De Gruyter, vol. 6(1), pages 298-308, December.
    • Handle: RePEc:vrs:demode:v:6:y:2018:i:1:p:298-308:n:17
    DOI: 10.1515/demo-2018-0017
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    References listed on IDEAS

    as
    1. 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.
    2. Durante Fabrizio & Fernández-Sánchez Juan & Trutschnig Wolfgang, 2014. "Solution to an open problem about a transformation on the space of copulas," Dependence Modeling, De Gruyter, vol. 2(1), pages 1-8, November.
    3. 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.
    4. repec:hal:wpaper:hal-00834000 is not listed on IDEAS
    5. Frederik Michiels & Ann De Schepper, 2012. "How to improve the fit of Archimedean copulas by means of transforms," Statistical Papers, Springer, vol. 53(2), pages 345-355, May.
    6. Christian Genest & Johanna Nešlehová & Noomen Ben Ghorbal, 2010. "Spearman's footrule and Gini's gamma: a review with complements," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(8), pages 937-954.
    7. Zhang, Ming-Heng, 2008. "Modelling total tail dependence along diagonals," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 73-80, February.
    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.
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    Keywords

    Copula; co-copula;

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