# 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

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topFuchs, 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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- Nelsen, R. B., 10.1007/s00362-006-0336-5, Statist. Papers 48 (2007), 329-336. Zbl1110.62071MR2295821DOI10.1007/s00362-006-0336-5
- Scarsini, M., On measures of concordance., Stochastica 8 (1984), 201-218. Zbl0582.62047MR0796650
- 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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