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Measures of concordance determined by D 4 -invariant copulas

Author

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  • H. H. Edwards
  • P. Mikusiński
  • M. D. Taylor

Abstract

A continuous random vector ( X , Y ) uniquely determines a copula C : [ 0 , 1 ] 2 → [ 0 , 1 ] such that when the distribution functions of X and Y are properly composed into C , the joint distribution function of ( X , Y ) results. A copula is said to be D 4 -invariant if its mass distribution is invariant with respect to the symmetries of the unit square. A D 4 -invariant copula leads naturally to a family of measures of concordance having a particular form, and all copulas generating this family are D 4 -invariant. The construction examined here includes Spearman’s rho and Gini’s measure of association as special cases.

Suggested Citation

  • H. H. Edwards & P. Mikusiński & M. D. Taylor, 2004. "Measures of concordance determined by D 4 -invariant copulas," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-9, January.
    • Handle: RePEc:hin:jijmms:593802
    DOI: 10.1155/S016117120440355X
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    Cited by:

    1. Damjana Kokol Bukovv{s}ek & Tomav{z} Kov{s}ir & Blav{z} Mojv{s}kerc & Matjav{z} Omladiv{c}, 2020. "Spearman's footrule and Gini's gamma: Local bounds for bivariate copulas and the exact region with respect to Blomqvist's beta," Papers 2009.06221, arXiv.org, revised Jan 2021.
    2. Martynas Manstavičius, 2022. "Diversity of Bivariate Concordance Measures," Mathematics, MDPI, vol. 10(7), pages 1-18, March.
    3. Claudio G. Borroni, 2019. "Mutual association measures," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 571-591, December.

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