Asymmetric semilinear copulas

Bernard De Baets; Hans De Meyer; Radko Mesiar

Kybernetika (2007)

  • Volume: 43, Issue: 2, page 221-233
  • ISSN: 0023-5954

Abstract

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We complement the recently introduced classes of lower and upper semilinear copulas by two new classes, called vertical and horizontal semilinear copulas, and characterize the corresponding class of diagonals. The new copulas are in essence asymmetric, with maximum asymmetry given by 1 / 16 . The only symmetric members turn out to be also lower and upper semilinear copulas, namely convex sums of Π and M .

How to cite

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De Baets, Bernard, De Meyer, Hans, and Mesiar, Radko. "Asymmetric semilinear copulas." Kybernetika 43.2 (2007): 221-233. <http://eudml.org/doc/33853>.

@article{DeBaets2007,
abstract = {We complement the recently introduced classes of lower and upper semilinear copulas by two new classes, called vertical and horizontal semilinear copulas, and characterize the corresponding class of diagonals. The new copulas are in essence asymmetric, with maximum asymmetry given by $1/16$. The only symmetric members turn out to be also lower and upper semilinear copulas, namely convex sums of $\Pi $ and $M$.},
author = {De Baets, Bernard, De Meyer, Hans, Mesiar, Radko},
journal = {Kybernetika},
keywords = {asymmetry; copula; diagonal section; semilinear copula; symmetry; asymmetry; diagonal section; semilinear copula; symmetry; characterizations},
language = {eng},
number = {2},
pages = {221-233},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Asymmetric semilinear copulas},
url = {http://eudml.org/doc/33853},
volume = {43},
year = {2007},
}

TY - JOUR
AU - De Baets, Bernard
AU - De Meyer, Hans
AU - Mesiar, Radko
TI - Asymmetric semilinear copulas
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 2
SP - 221
EP - 233
AB - We complement the recently introduced classes of lower and upper semilinear copulas by two new classes, called vertical and horizontal semilinear copulas, and characterize the corresponding class of diagonals. The new copulas are in essence asymmetric, with maximum asymmetry given by $1/16$. The only symmetric members turn out to be also lower and upper semilinear copulas, namely convex sums of $\Pi $ and $M$.
LA - eng
KW - asymmetry; copula; diagonal section; semilinear copula; symmetry; asymmetry; diagonal section; semilinear copula; symmetry; characterizations
UR - http://eudml.org/doc/33853
ER -

References

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  1. Bertino S., On dissimilarity between cyclic permutations, Metron 35 (1977), 53–88, in Italian (1977) MR0600402
  2. Durante F., Mesiar, R., Sempi C., On a family of copulas constructed from the diagonal section, Soft Computing 10 (2006), 490–494 Zbl1098.60016
  3. Durante F., Kolesárová A., Mesiar, R., Sempi C., Semilinear copulas, Submitted 
  4. Durante F., Kolesárová A., Mesiar, R., Sempi C., Copulas with given diagonal sections: novel constructions and applications, Submitted Zbl1158.62324
  5. Joe H., Multivariate Models and Dependence Concepts, Chapman & Hall, London 1997 Zbl0990.62517MR1462613
  6. Klement E. P., Kolesárová A., Extensions to copulas and quasi-copulas as special 1-Lipschitz aggregation operators, Kybernetika 41 (2005), 329–348 MR2181422
  7. Klement E. P., Mesiar R., How non-symmetric can a copula be? Comment, Math. Univ. Carolinae 47 (2006), 141–148 MR2223973
  8. Nelsen R. B., An Introduction to Copulas, Lecture Notes in Statistics 139, Springer, New York 1999. Second edition. Springer Series in Statistics, Springer, New York 2006 (1999) Zbl0909.62052MR2197664
  9. Nelsen R. B., Extremes of nonexchangeability, Stat. Papers 48 (2007), 329–336 Zbl1110.62071MR2295821
  10. Nelsen R. B., Fredricks G. A., Diagonal copulas, In: Distributions with given Marginals and Moment Problems (V. Beneš and J. Štěpán, eds.), Kluwer Academic Publishers, Dordrecht 1977, pp. 121–127 (1977) MR1614665
  11. Nelsen R. B., Quesada-Molina J. J., Rodríguez-Lallena J. A., Úbeda-Flores M., On the construction of copulas and quasi-copulas with given diagonal sections, Insurance Math. Econom., in press Zbl1152.60311
  12. Sklar A., Fonctions de répartition á n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris 8 (1959), 229–231 (1959) MR0125600

Citations in EuDML Documents

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  1. Tarad Jwaid, Bernard de Baets, Hans de Meyer, Orbital semilinear copulas
  2. Juan Fernández Sánchez, Manuel Úbeda-Flores, On copulas that generalize semilinear copulas
  3. Gaspar Mayor, Radko Mesiar, Joan Torrens, On quasi-homogeneous copulas
  4. Fabrizio Durante, Juan Fernández-Sánchez, A note on biconic copulas
  5. Sebastian Fuchs, Klaus D. Schmidt, Bivariate copulas: Transformations, asymmetry and measures of concordance
  6. Fabrizio Durante, Pier Luigi Papini, Componentwise concave copulas and their asymmetry

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