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On order statistics and Kendall’s tau

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  • Fuchs, Sebastian
  • Schmidt, Klaus D.

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.

Suggested Citation

  • Fuchs, Sebastian & Schmidt, Klaus D., 2021. "On order statistics and Kendall’s tau," Statistics & Probability Letters, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:stapro:v:169:y:2021:i:c:s0167715220302753
    DOI: 10.1016/j.spl.2020.108972
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    References listed on IDEAS

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    1. Durante, Fabrizio & Fernández-Sánchez, Juan, 2010. "Multivariate shuffles and approximation of copulas," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1827-1834, December.
    2. Nelsen, Roger B. & Quesada-Molina, José Juan & Rodríguez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2003. "Kendall distribution functions," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 263-268, November.
    3. Sebastian Fuchs & Yann McCord & Klaus D. Schmidt, 2018. "Characterizations of Copulas Attaining the Bounds of Multivariate Kendall’s Tau," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 424-438, August.
    4. Navarro, Jorge & Spizzichino, Fabio, 2010. "On the relationships between copulas of order statistics and marginal distributions," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 473-479, March.
    5. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
    6. Jae Youn Ahn & Sebastian Fuchs, 2020. "On Minimal Copulas under the Concordance Order," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 762-780, March.
    7. Dietz, Markus & Fuchs, Sebastian & Schmidt, Klaus D., 2016. "On order statistics and their copulas," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 165-172.
    8. Genest, Christian & Rivest, Louis-Paul, 2001. "On the multivariate probability integral transformation," Statistics & Probability Letters, Elsevier, vol. 53(4), pages 391-399, July.
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    Cited by:

    1. Zachariah, Swaroop Georgy & Arshad, Mohd. & Pathak, Ashok Kumar, 2024. "A new class of copulas having dependence range larger than FGM-type copulas," Statistics & Probability Letters, Elsevier, vol. 206(C).

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