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Examples for the coefficient of tail dependence and the domain of attraction of a bivariate extreme value distribution

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  • Schlather, Martin

Abstract

The tail behaviour of many bivariate distributions with unit Fréchet margins can be characterised by the coefficient of tail dependence and a slowly varying function. We show that such a characterisation is not always possible, and neither implies nor is implied by the fact that the distribution belongs to the domain of attraction of a bivariate extreme value distribution.

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  • Schlather, Martin, 2001. "Examples for the coefficient of tail dependence and the domain of attraction of a bivariate extreme value distribution," Statistics & Probability Letters, Elsevier, vol. 53(3), pages 325-329, June.
    • Handle: RePEc:eee:stapro:v:53:y:2001:i:3:p:325-329
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    References listed on IDEAS

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    1. Anthony W. Ledford & Jonathan A. Tawn, 1997. "Modelling Dependence within Joint Tail Regions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 475-499.
    2. P. Bortot & S. Coles & J. Tawn, 2000. "The multivariate Gaussian tail model: an application to oceanographic data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(1), pages 31-049.
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    1. Einmahl, J.H.J. & de Haan, L.F.M. & Li, D., 2004. "Weighted Approximations of Tail Copula Processes with Application to Testing the Multivariate Extreme Value Condition," Other publications TiSEM 0b2c1bfa-d609-494a-8929-8, Tilburg University, School of Economics and Management.
    2. Wu, Lifan & Samorodnitsky, Gennady, 2020. "Regularly varying random fields," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4470-4492.
    3. Dutfoy Anne & Parey Sylvie & Roche Nicolas, 2014. "Multivariate Extreme Value Theory - A Tutorial with Applications to Hydrology and Meteorology," Dependence Modeling, De Gruyter, vol. 2(1), pages 1-19, June.
    4. Di Bernardino, Elena & Maume-Deschamps, Véronique & Prieur, Clémentine, 2013. "Estimating a bivariate tail: A copula based approach," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 81-100.
    5. Schmid, Friedrich & Schmidt, Rafael, 2007. "Multivariate conditional versions of Spearman's rho and related measures of tail dependence," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1123-1140, July.
    6. Elena Di Bernardino & Didier Rullière, 2016. "On tail dependence coefficients of transformed multivariate Archimedean copulas," Post-Print hal-00992707, HAL.
    7. Einmahl, J.H.J. & de Haan, L.F.M. & Li, D., 2006. "Weighted approximations of tail copula processes with applications to testing the bivariate extreme value condition," Other publications TiSEM 18b65ac3-ba79-4bff-ad53-2, Tilburg University, School of Economics and Management.

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