How non-symmetric can a copula be?

Erich Peter Klement; Radko Mesiar

Commentationes Mathematicae Universitatis Carolinae (2006)

  • Volume: 47, Issue: 1, page 141-148
  • ISSN: 0010-2628

Abstract

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A two-place function measuring the degree of non-symmetry for (quasi-)copulas is considered. We construct copulas which are maximally non-symmetric on certain subsets of the unit square. It is shown that there is no copula (and no quasi-copula) which is maximally non-symmetric on the whole unit square.

How to cite

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Klement, Erich Peter, and Mesiar, Radko. "How non-symmetric can a copula be?." Commentationes Mathematicae Universitatis Carolinae 47.1 (2006): 141-148. <http://eudml.org/doc/249851>.

@article{Klement2006,
abstract = {A two-place function measuring the degree of non-symmetry for (quasi-)copulas is considered. We construct copulas which are maximally non-symmetric on certain subsets of the unit square. It is shown that there is no copula (and no quasi-copula) which is maximally non-symmetric on the whole unit square.},
author = {Klement, Erich Peter, Mesiar, Radko},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {copula; quasi-copula; symmetry; opposite diagonal; quasi-copula; symmetry; opposite diagonal},
language = {eng},
number = {1},
pages = {141-148},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {How non-symmetric can a copula be?},
url = {http://eudml.org/doc/249851},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Klement, Erich Peter
AU - Mesiar, Radko
TI - How non-symmetric can a copula be?
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 1
SP - 141
EP - 148
AB - A two-place function measuring the degree of non-symmetry for (quasi-)copulas is considered. We construct copulas which are maximally non-symmetric on certain subsets of the unit square. It is shown that there is no copula (and no quasi-copula) which is maximally non-symmetric on the whole unit square.
LA - eng
KW - copula; quasi-copula; symmetry; opposite diagonal; quasi-copula; symmetry; opposite diagonal
UR - http://eudml.org/doc/249851
ER -

References

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  5. Klement E.P., Kolesárová A., Extension to copulas and quasi-copulas as special 1 -Lipschitz aggregation operators, Kybernetika (Prague) 41 (2005), 329-348. (2005) MR2181422
  6. Klement E.P., Mesiar R., Pap E., Triangular Norms, Kluwer Academic Publishers, Dordrecht, 2000. Zbl1087.20041MR1790096
  7. Klement E.P., Mesiar R., Pap E., Archimax copulas and invariance under transformations, C.R. Math. Acad. Sci. Paris 340 (2005), 755-758. (2005) Zbl1126.62040MR2141065
  8. Mikusiński P., Taylor M.D., A remark on associative copulas, Comment. Math. Univ. Carolinae 40 (1999), 789-793. (1999) MR1756554
  9. Nelsen R.B., An introduction to copulas, Lecture Notes in Statistics 139, Springer, New York, 1999. Zbl1152.62030MR1653203
  10. Schweizer B., Sklar A., Probabilistic Metric Spaces, North-Holland, New York, 1983. Zbl0546.60010MR0790314
  11. Sklar A., Fonctions de répartition à n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris 8 (1959), 229-231. (1959) MR0125600
  12. Sklar A., Random variables, joint distribution functions, and copulas, Kybernetika (Prague) 9 (1973), 449-460. (1973) Zbl0292.60036MR0345164

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