Bivariate copulas: Transformations, asymmetry and measures of concordance

Sebastian Fuchs; Klaus D. Schmidt

Kybernetika (2014)

  • Volume: 50, Issue: 1, page 109-125
  • ISSN: 0023-5954

Abstract

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The present paper introduces a group of transformations on the collection of all bivariate copulas. This group contains an involution which is particularly useful since it provides (1) a criterion under which a given symmetric copula can be transformed into an asymmetric one and (2) a condition under which for a given copula the value of every measure of concordance is equal to zero. The group also contains a subgroup which is of particular interest since its four elements preserve symmetry, the order between two copulas and the value of every measure of concordance.

How to cite

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Fuchs, Sebastian, and Schmidt, Klaus D.. "Bivariate copulas: Transformations, asymmetry and measures of concordance." Kybernetika 50.1 (2014): 109-125. <http://eudml.org/doc/261153>.

@article{Fuchs2014,
abstract = {The present paper introduces a group of transformations on the collection of all bivariate copulas. This group contains an involution which is particularly useful since it provides (1) a criterion under which a given symmetric copula can be transformed into an asymmetric one and (2) a condition under which for a given copula the value of every measure of concordance is equal to zero. The group also contains a subgroup which is of particular interest since its four elements preserve symmetry, the order between two copulas and the value of every measure of concordance.},
author = {Fuchs, Sebastian, Schmidt, Klaus D.},
journal = {Kybernetika},
keywords = {bivariate copulas; transformations; asymmetry; measures of concordance; bivariate copulas; transformations; asymmetry; measures of concordance},
language = {eng},
number = {1},
pages = {109-125},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Bivariate copulas: Transformations, asymmetry and measures of concordance},
url = {http://eudml.org/doc/261153},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Fuchs, Sebastian
AU - Schmidt, Klaus D.
TI - Bivariate copulas: Transformations, asymmetry and measures of concordance
JO - Kybernetika
PY - 2014
PB - Institute of Information Theory and Automation AS CR
VL - 50
IS - 1
SP - 109
EP - 125
AB - The present paper introduces a group of transformations on the collection of all bivariate copulas. This group contains an involution which is particularly useful since it provides (1) a criterion under which a given symmetric copula can be transformed into an asymmetric one and (2) a condition under which for a given copula the value of every measure of concordance is equal to zero. The group also contains a subgroup which is of particular interest since its four elements preserve symmetry, the order between two copulas and the value of every measure of concordance.
LA - eng
KW - bivariate copulas; transformations; asymmetry; measures of concordance; bivariate copulas; transformations; asymmetry; measures of concordance
UR - http://eudml.org/doc/261153
ER -

References

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  1. Baets, B. De, Meyer, H. De, Mesiar, R., Asymmetric semilinear copulas., Kybernetika 43 (2007), 221-233. Zbl1136.62350MR2343397
  2. Durante, F., Papini, P. L., Componentwise concave copulas and their asymmetry., Kybernetika 45 (2009), 1003-1011. Zbl1191.62095MR2650079
  3. Durante, F., Sempi, C., Copula theory - an introduction., In: Copula Theory and Its Applications (P. Jaworski, F. Durante, W. K. Härdle and T. Rychlik, eds.), Springer, Berlin, Heidelberg 2010, pp. 3-31. MR3051261
  4. Edwards, H. H., Mikusiński, P., Taylor, M. D., 10.1155/S016117120440355X, Internat. J. Math. Sci. 70 (2004), 3867-3875. Zbl1075.62042MR2129414DOI10.1155/S016117120440355X
  5. Fuchs, S., Multivariate copulas - Transformations, symmetry, order and measures of concordance., Submitted for publication (2013). 
  6. Klement, E. P., Mesiar, R., Pap, E., Invariant copulas., Kybernetika 38 (2002), 275-285. Zbl1264.62045MR1944309
  7. Liebscher, E., 10.1016/j.jmva.2008.02.025, J. Multivariate Anal. 99 (2008), 2234-2250. Zbl1151.62043MR2463386DOI10.1016/j.jmva.2008.02.025
  8. Nelsen, R. B., An Introduction to Copulas. Second edition., Springer, New York 2006. MR2197664
  9. Nelsen, R. B., 10.1007/s00362-006-0336-5, Statist. Papers 48 (2007), 329-336. Zbl1110.62071MR2295821DOI10.1007/s00362-006-0336-5
  10. Scarsini, M., On measures of concordance., Stochastica 8 (1984), 201-218. Zbl0582.62047MR0796650
  11. Taylor, M. D., 10.1007/s10463-006-0076-2, Ann. Inst. Statist. Math. 59 (2007), 789-806. Zbl1131.62054MR2397737DOI10.1007/s10463-006-0076-2

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