On order statistics and Kendall's tau

Sebastian Fuchs, Klaus D. Schmidt

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number108972
JournalStatistics and Probability Letters
Volume169
Issue number169
DOIs
Publication statusPublished - Feb 2021

Keywords

  • Copula
  • Kendall's distribution function
  • Kendall's tau
  • Order statistic
  • Probability of concordance

Fields of Science and Technology Classification 2012

  • 101 Mathematics

Cite this