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On Extreme Value Copulas with Given Concordance Measures

  • Piotr JaworskiEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 981)

Abstract

The dependence measures, like for example Kendall tau, Spearman rho, Blomquist beta or tail dependence coefficient, are the main numerical characterization of Bivariate Extreme Value Copulas. Such copulas are characterized by a function on the unit segment, called a Pickands dependence function, which is convex and comprised between two bounds. We identify the smallest possible compact sets containing the graphs of all Pickands dependence functions whose corresponding bivariate extreme-value copula has fixed values of given dependence measures. Moreover we provide the bounds for such bivariate extreme-value copulas.

Keywords

Extreme value copulas Pickands functions Kendall \(\tau \) Spearman \(\rho \) Tail dependence coefficient 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of WarsawWarsawPoland

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