On order statistics and Kendall's tau

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Abstract

Using Kendall's tau for copulas, we compare the degree of concordance of random variables with that of their order statistics. We prove a general inequality and show that this inequality is strict for every copula from the Fréchet family which is distinct from the upper Fréchet–Hoeffding bound.

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Fuchs, S., & Schmidt, K. D. (2021). On order statistics and Kendall’s tau. Statistics and Probability Letters, 169. https://doi.org/10.1016/j.spl.2020.108972

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