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 |
References:
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| [3] | Fuchs, S., Schmidt, K. D.: Bivariate copulas: Transformations, asymmetry and measure of concordance. Kybernetika 50 (2013), 109-125. · Zbl 1398.60025 |
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| [5] | Taylor, M. D.: Multivariate measures of concordance. Ann. Inst. Statist. Math. 59 (2007), 789-806. · Zbl 1131.62054 · doi:10.1007/s10463-006-0076-2 |
| [6] | Taylor, M. D.: Some properties of multivariate measures of concordance. arXiv:0808.3105 (2008). |
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| [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 · doi:10.1007/BF02915438 |
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