Extension to copulas and quasi-copulas as special 1 -Lipschitz aggregation operators

Erich Peter Klement; Anna Kolesárová

Kybernetika (2005)

  • Volume: 41, Issue: 3, page [329]-348
  • ISSN: 0023-5954

Abstract

top
Smallest and greatest 1 -Lipschitz aggregation operators with given diagonal section, opposite diagonal section, and with graphs passing through a single point of the unit cube, respectively, are determined. These results are used to find smallest and greatest copulas and quasi-copulas with these properties (provided they exist).

How to cite

top

Klement, Erich Peter, and Kolesárová, Anna. "Extension to copulas and quasi-copulas as special $1$-Lipschitz aggregation operators." Kybernetika 41.3 (2005): [329]-348. <http://eudml.org/doc/33757>.

@article{Klement2005,
abstract = {Smallest and greatest $1$-Lipschitz aggregation operators with given diagonal section, opposite diagonal section, and with graphs passing through a single point of the unit cube, respectively, are determined. These results are used to find smallest and greatest copulas and quasi-copulas with these properties (provided they exist).},
author = {Klement, Erich Peter, Kolesárová, Anna},
journal = {Kybernetika},
keywords = {copula; quasi-copula; $1$-Lipschitz aggregation operator; diagonal; copula; quasi-copula; 1-Lipschitz aggregation operator; diagonal},
language = {eng},
number = {3},
pages = {[329]-348},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Extension to copulas and quasi-copulas as special $1$-Lipschitz aggregation operators},
url = {http://eudml.org/doc/33757},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Klement, Erich Peter
AU - Kolesárová, Anna
TI - Extension to copulas and quasi-copulas as special $1$-Lipschitz aggregation operators
JO - Kybernetika
PY - 2005
PB - Institute of Information Theory and Automation AS CR
VL - 41
IS - 3
SP - [329]
EP - 348
AB - Smallest and greatest $1$-Lipschitz aggregation operators with given diagonal section, opposite diagonal section, and with graphs passing through a single point of the unit cube, respectively, are determined. These results are used to find smallest and greatest copulas and quasi-copulas with these properties (provided they exist).
LA - eng
KW - copula; quasi-copula; $1$-Lipschitz aggregation operator; diagonal; copula; quasi-copula; 1-Lipschitz aggregation operator; diagonal
UR - http://eudml.org/doc/33757
ER -

References

top
  1. Alsina C., Nelsen R. B., Schweizer B., 10.1016/0167-7152(93)90001-Y, Statist. Probab. Lett. 17 (1993), 85–89 (1993) Zbl0798.60023MR1223530DOI10.1016/0167-7152(93)90001-Y
  2. Bertino S., On dissimilarity between cyclic permutations, Metron 35 (1977), 53–88. In Italian (1977) MR0600402
  3. Calvo T., Kolesárová A., Komorníková, M., Mesiar R., Aggregation operators: properties, classes and construction methods, In: Aggregation Operators. New Trends and Applications (T. Calvo, G. Mayor, and R. Mesiar, eds.), Physica–Verlag, Heidelberg 2002, pp. 3–104 Zbl1039.03015MR1936383
  4. Durante F., Mesiar, R., Sempi C., On a family of copulas constructed from the diagonal section, Soft Computing (accepted for publication) Zbl1098.60016
  5. Frank M. J., 10.1007/BF02189866, Aequationes Math. 19 (1979), 194–226 (1979) Zbl0444.39003MR0556722DOI10.1007/BF02189866
  6. Frank M. J., Diagonals of copulas and Schröder’s equation, Aequationes Math. 51 (1996), 150 (1996) 
  7. Fredricks G. A., Nelsen R. B., Copulas constructed from diagonal sections, In: Distributions with Given Marginals and Moment Problems (V. Beneš and J. Štěpán, eds.), Kluwer Academic Publishers, Dordrecht 1997, pp. 129–136 (1997) Zbl0906.60022MR1614666
  8. Fredricks G. A., Nelsen R. B., The Bertino family of copulas, In: Distributions with Given Marginals and Statistical Modelling (C. M. Cuadras, J. Fortiana, and J. A. Rodríguez-Lallena, eds.), Kluwer Academic Publishers, Dordrecht 2002, pp. 81–91 Zbl1135.62334MR2058982
  9. Genest C., Molina J. J. Quesada, Lallena J. A. Rodríguez, Sempi C., 10.1006/jmva.1998.1809, J. Multivariate Anal. 69 (1999) 193–205 (1999) MR1703371DOI10.1006/jmva.1998.1809
  10. Klement E. P., Mesiar, R., Pap E., Triangular Norms, Kluwer Academic Publishers, Dordrecht 2000 Zbl1087.20041MR1790096
  11. Kolesárová A., 1 -Lipschitz aggregation operators and quasi-copulas, Kybernetika 39 (2003), 615–629 MR2042344
  12. Kolesárová A., Mordelová J., 1 -Lipschitz and kernel aggregation operators, In: Proc. AGOP ’2001, Oviedo 2001, pp. 71–76 
  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. 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 1997, pp. 121–127 (1997) Zbl0906.60021MR1614665
  15. Nelsen R. B., Molina J. J. Quesada, Lallena J. A. Rodríguez, Flores M. Úbeda, 10.1016/j.jmva.2003.09.002, J. Multivariate Anal. 90 (2004), 348–358 MR2081783DOI10.1016/j.jmva.2003.09.002
  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. Sklar A., Random variables, joint distribution functions, and copulas, Kybernetika 9 (1973), 449–460 (1973) Zbl0292.60036MR0345164
  19. Sungur E. A., Yang Y., 10.1080/03610929608831791, Comm. Statist. Theory Methods 25 (1996), 1659–1676 (1996) Zbl0900.62339MR1411104DOI10.1080/03610929608831791

Citations in EuDML Documents

top
  1. Bernard De Baets, Hans De Meyer, Radko Mesiar, Asymmetric semilinear copulas
  2. Erich Peter Klement, Radko Mesiar, How non-symmetric can a copula be?
  3. Manuel Úbeda-Flores, A new family of trivariate proper quasi-copulas
  4. Gaspar Mayor, Radko Mesiar, Joan Torrens, On quasi-homogeneous copulas
  5. Fabrizio Durante, Anna Kolesárová, Radko Mesiar, Carlo Sempi, Copulas with given values on a horizontal and a vertical section
  6. José Antonio Rodríguez–Lallena, Manuel Úbeda-Flores, Quasi-copulas with quadratic sections in one variable

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.