Transformations of copulas

Erich Peter Klement; Radko Mesiar; Endre Pap

Kybernetika (2005)

  • Volume: 41, Issue: 4, page [425]-434
  • ISSN: 0023-5954

Abstract

top
Transformations of copulas by means of increasing bijections on the unit interval and attractors of copulas are discussed. The invariance of copulas under such transformations as well as the relationship to maximum attractors and Archimax copulas is investigated.

How to cite

top

Klement, Erich Peter, Mesiar, Radko, and Pap, Endre. "Transformations of copulas." Kybernetika 41.4 (2005): [425]-434. <http://eudml.org/doc/33764>.

@article{Klement2005,
abstract = {Transformations of copulas by means of increasing bijections on the unit interval and attractors of copulas are discussed. The invariance of copulas under such transformations as well as the relationship to maximum attractors and Archimax copulas is investigated.},
author = {Klement, Erich Peter, Mesiar, Radko, Pap, Endre},
journal = {Kybernetika},
keywords = {copula; transformation of copulas; invariant copulas; maximum attractor; Archimax copula; transformation of copulas; invariant copulas; maximum attractor; Archimax copula},
language = {eng},
number = {4},
pages = {[425]-434},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Transformations of copulas},
url = {http://eudml.org/doc/33764},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Klement, Erich Peter
AU - Mesiar, Radko
AU - Pap, Endre
TI - Transformations of copulas
JO - Kybernetika
PY - 2005
PB - Institute of Information Theory and Automation AS CR
VL - 41
IS - 4
SP - [425]
EP - 434
AB - Transformations of copulas by means of increasing bijections on the unit interval and attractors of copulas are discussed. The invariance of copulas under such transformations as well as the relationship to maximum attractors and Archimax copulas is investigated.
LA - eng
KW - copula; transformation of copulas; invariant copulas; maximum attractor; Archimax copula; transformation of copulas; invariant copulas; maximum attractor; Archimax copula
UR - http://eudml.org/doc/33764
ER -

References

top
  1. Aczél J., Alsina C., Characterizations of some classes of quasilinear functions with applications to triangular norms and to synthesizing judgements, Methods Oper. Res. 48 (1984) 3–22 (1984) Zbl0527.39002MR0736352
  2. Ali M. M., Mikhail N. N., Haq M. S., 10.1016/0047-259X(78)90063-5, J. Multivariate Anal. 8 (1978), 405–412 (1978) MR0512610DOI10.1016/0047-259X(78)90063-5
  3. Alsina C., Frank M. J., Schweizer B., Associative Functions on Intervals: A Primer on Triangular Norms, in pres 
  4. Calvo T., Mayor, G., (eds.) R. Mesiar, Aggregation Operators, New Trends and Applications. Physica–Verlag, Heidelberg 2002 Zbl0983.00020MR1936383
  5. Capéraà P., Fougères A.-L., Genest C., 10.1006/jmva.1999.1845, J. Multivariate Anal. 72 (2000), 30–49 Zbl0978.62043MR1747422DOI10.1006/jmva.1999.1845
  6. Cuculescu I., Theodorescu R., 10.1016/S1631-073X(02)02322-1, C. R. Math. Acad. Sci. Paris 334 (2002) 689–692 Zbl0996.60026MR1903371DOI10.1016/S1631-073X(02)02322-1
  7. Galambos J., The Asymptotic Theory of Extreme Order Statistics, Robert E. Krieger Publishing, Melbourne 1987 Zbl0634.62044MR0936631
  8. Genest C., Rivest L.-P., 10.1016/0167-7152(89)90123-5, Statist. Probab. Lett. 8 (1989), 207–211 (1989) Zbl0701.62060MR1024029DOI10.1016/0167-7152(89)90123-5
  9. Klement E. P., Mesiar, R., Pap E., Triangular Norms, Kluwer, Dordrecht 2000 Zbl1087.20041MR1790096
  10. Klement E. P., Mesiar, R., Pap E., 10.1016/j.crma.2005.04.012, C. R. Math. Acad. Sci. Paris 340 (2005), 755–758 Zbl1126.62040MR2141065DOI10.1016/j.crma.2005.04.012
  11. Klir G. J., Folger T. A., Fuzzy Sets, Uncertainty, and Information, Prentice Hall, Englewood Cliffs, NJ 1988 Zbl0675.94025MR0930102
  12. Mikusiński P., Taylor M. D., A remark on associative copulas, Comment. Math. Univ. Carolin. 40 (1999), 789–793 (1999) MR1756554
  13. Nelsen R. B., 10.1007/978-1-4757-3076-0, (Lecture Notes in Statistics 139.) Springer, New York 1999 Zbl1152.62030MR1653203DOI10.1007/978-1-4757-3076-0
  14. Pickands J., Multivariate extreme value distributions, Bull. Inst. Internat. Statist. 49 (1981), 859–878 (with a discussion, 894–902) (1981) Zbl0518.62045MR0820979
  15. Rückschlossová T., Aggregation Operators and Invariantness, Ph.D. Thesis, Slovak University of Technology, Bratislava 2003 
  16. Schweizer B., Sklar A., Probabilistic Metric Spaces, North–Holland, New York 1983 Zbl0546.60010MR0790314
  17. Sklar A., Fonctions de répartition à n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris 8 (1959), 229–231 (1959) MR0125600
  18. Tawn J. A., 10.1093/biomet/75.3.397, Biometrika 75 (1988), 397–415 (1988) Zbl0653.62045MR0967580DOI10.1093/biomet/75.3.397

Citations in EuDML Documents

top
  1. Arthur Charpentier, Dynamic dependence ordering for Archimedean copulas and distorted copulas
  2. Fabrizio Durante, Juan Fernández-Sánchez, Wolfgang Trutschnig, Solution to an open problem about a transformation on the space of copulas
  3. Elena Di Bernardino, Didier Rullière, On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators
  4. Fabrizio Durante, Anna Kolesárová, Radko Mesiar, Carlo Sempi, Copulas with given values on a horizontal and a vertical section
  5. Ali Dolati, Manuel Úbeda-Flores, Constructing copulas by means of pairs of order statistics
  6. Michal Dibala, Susanne Saminger-Platz, Radko Mesiar, Erich Peter Klement, Defects and transformations of quasi-copulas
  7. Fabrizio Durante, Pier Luigi Papini, Componentwise concave copulas and their asymmetry

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.