A sharp inequality for Kendall's $\tau$ and Spearman's $\rho$ of Extreme-Value Copulas

Thomas Mroz; Wolfgang Trutschnig

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arXiv · 1811.02256

A sharp inequality for Kendall's $\tau$ and Spearman's $\rho$ of Extreme-Value Copulas

Thomas Mroz·Wolfgang Trutschnig

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Abstract

We derive a new (lower) inequality between Kendall's tau? and Spearman's rho? for two-dimensional Extreme-Value Copulas, show that this inequality is sharp in each point and conclude that the comonotonic and the product copula are the only Extreme-Value Copulas for which the well-known lower Hutchinson-Lai inequality is sharp.

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Thomas Mroz, Wolfgang Trutschnig. 2018-11-06. A sharp inequality for Kendall's $\tau$ and Spearman's $\rho$ of Extreme-Value Copulas. https://arxiv.org/abs/1811.02256

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