Multivariate copulas: Transformations, symmetry, order and measures of concordance

Sebastian Fuchs

Kybernetika (2014)

  • Volume: 50, Issue: 5, page 725-743
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Fuchs, Sebastian. "Multivariate copulas: Transformations, symmetry, order and measures of concordance." Kybernetika 50.5 (2014): 725-743. <http://eudml.org/doc/262157>.

@article{Fuchs2014,
abstract = {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.},
author = {Fuchs, Sebastian},
journal = {Kybernetika},
keywords = {multivariate copulas; transformations; symmetry; order; measures of concordance; multivariate copulas; transformations; symmetry; order; measures of concordance},
language = {eng},
number = {5},
pages = {725-743},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Multivariate copulas: Transformations, symmetry, order and measures of concordance},
url = {http://eudml.org/doc/262157},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Fuchs, Sebastian
TI - Multivariate copulas: Transformations, symmetry, order and measures of concordance
JO - Kybernetika
PY - 2014
PB - Institute of Information Theory and Automation AS CR
VL - 50
IS - 5
SP - 725
EP - 743
AB - 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.
LA - eng
KW - multivariate copulas; transformations; symmetry; order; measures of concordance; multivariate copulas; transformations; symmetry; order; measures of concordance
UR - http://eudml.org/doc/262157
ER -

References

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  1. Durante, F., Sempi, C., Copula theory: an introduction., In: Copula Theory and Its Applications (P. Jaworski, F. Durante, W. Häerdle, T. Rychlik, eds.), Springer, Berlin, Heidelberg 2010, pp. 3-31. MR3051261
  2. Dolati, A., Úbeda-Flores, M., On measures of multivariate concordance., J. Probab. Stat. Sci. 4 (2006), 147-163. MR2488161
  3. Fuchs, S., Schmidt, K. D., Bivariate copulas: Transformations, asymmetry and measure of concordance., Kybernetika 50 (2013), 109-125. MR3195007
  4. Nelsen, R. B., An Introduction to Copulas. Second Edition., Springer, New York 2006. MR2197664
  5. Taylor, M. D., 10.1007/s10463-006-0076-2, Ann. Inst. Statist. Math. 59 (2007), 789-806. Zbl1131.62054MR2397737DOI10.1007/s10463-006-0076-2
  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). MR2397737
  8. Úbeda-Flores, M., 10.1007/BF02915438, Ann. Inst. Statist. Math. 57 (2005) 781-788. Zbl1093.62060MR2213491DOI10.1007/BF02915438

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