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Multivariate copulas: transformations, symmetry, order and measures of concordance. (English) Zbl 1321.60018
Summary: The present paper introduces a group of transformations on the collection of all multivariate copulas. The group contains a subgroup which is of particular interest since its elements preserve symmetry, the concordance order between two copulas and the value of every measure of concordance.

MSC:
60E05 Probability distributions: general theory
62E10 Characterization and structure theory of statistical distributions
62H20 Measures of association (correlation, canonical correlation, etc.)
20C99 Representation theory of groups
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[1] Durante, F., Sempi, C.: Copula theory: an introduction. Copula Theory and Its Applications (P. Jaworski, F. Durante, W. Häerdle, T. Rychlik, Springer, Berlin, Heidelberg 2010, pp. 3-31.
[2] Dolati, A., Úbeda-Flores, M.: On measures of multivariate concordance. J. Probab. Stat. Sci. 4 (2006), 147-163. · Zbl 1143.62321
[3] Fuchs, S., Schmidt, K. D.: Bivariate copulas: Transformations, asymmetry and measure of concordance. Kybernetika 50 (2013), 109-125. · Zbl 1398.60025
[4] Nelsen, R. B.: An Introduction to Copulas. Second Edition. Springer, New York 2006. · Zbl 1152.62030
[5] Taylor, M. D.: Multivariate measures of concordance. Ann. Inst. Statist. Math. 59 (2007), 789-806. · Zbl 1131.62054
[6] Taylor, M. D.: Some properties of multivariate measures of concordance. arXiv:0808.3105 (2008).
[7] Taylor, M. D.: Multivariate measures of concordance for copulas and their marginals. arXiv:1004.5023 (2010). · Zbl 1349.62244
[8] Úbeda-Flores, M.: Multivariate versions of Blomqvist’s beta and Spearman’s footrule. Ann. Inst. Statist. Math. 57 (2005) 781-788. · Zbl 1093.62060
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