On order statistics and Kendall’s tau

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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Bibliographic Details
Published inStatistics & probability letters Vol. 169; p. 108972
Main Authors Fuchs, Sebastian, Schmidt, Klaus D.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.02.2021
Subjects
Copula
Kendall’s distribution function
Kendall’s tau
Order statistic
Probability of concordance
Order statistic
Probability of concordance
Copula
Kendall’s tau
Kendall’s distribution function
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Summary: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.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2020.108972