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A Biconvex Form for Copulas

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  • Fuchs Sebastian

    (Lehrstuhl für Versicherungsmathematik, Technische Universität Dresden)

Abstract

We study the integration of a copula with respect to the probability measure generated by another copula. To this end, we consider the map [. , .] : C × C → R given bywhere C denotes the collection of all d–dimensional copulas and QD denotes the probability measures associated with the copula D. Specifically, this is of interest since several measures of concordance such as Kendall’s tau, Spearman’s rho and Gini’s gamma can be expressed in terms of the map [. , .]. Quite generally, the map [. , .] can be applied to construct and investigate measures of concordance.

Suggested Citation

  • Fuchs Sebastian, 2016. "A Biconvex Form for Copulas," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-13, February.
    • Handle: RePEc:vrs:demode:v:4:y:2016:i:1:p:13:n:3
    DOI: 10.1515/demo-2016-0003
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    References listed on IDEAS

    as
    1. Marco Scarsini, 1984. "Strong measures of concordance and convergence in probability," Post-Print hal-00542387, HAL.
    2. Marco Scarsini, 1984. "On measures of concordance," Post-Print hal-00542380, HAL.
    3. M. Taylor, 2007. "Multivariate measures of concordance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(4), pages 789-806, December.
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