Quasi-copulas with quadratic sections in one variable

José Antonio Rodríguez–Lallena; Manuel Úbeda-Flores

Kybernetika (2008)

  • Volume: 44, Issue: 6, page 879-890
  • ISSN: 0023-5954

Abstract

top
We introduce and characterize the class of multivariate quasi-copulas with quadratic sections in one variable. We also present and analyze examples to illustrate our results.

How to cite

top

Rodríguez–Lallena, José Antonio, and Úbeda-Flores, Manuel. "Quasi-copulas with quadratic sections in one variable." Kybernetika 44.6 (2008): 879-890. <http://eudml.org/doc/33971>.

@article{Rodríguez2008,
abstract = {We introduce and characterize the class of multivariate quasi-copulas with quadratic sections in one variable. We also present and analyze examples to illustrate our results.},
author = {Rodríguez–Lallena, José Antonio, Úbeda-Flores, Manuel},
journal = {Kybernetika},
keywords = {1-Lipschitz condition; copula; quasi-copula; quadratic sections},
language = {eng},
number = {6},
pages = {879-890},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Quasi-copulas with quadratic sections in one variable},
url = {http://eudml.org/doc/33971},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Rodríguez–Lallena, José Antonio
AU - Úbeda-Flores, Manuel
TI - Quasi-copulas with quadratic sections in one variable
JO - Kybernetika
PY - 2008
PB - Institute of Information Theory and Automation AS CR
VL - 44
IS - 6
SP - 879
EP - 890
AB - We introduce and characterize the class of multivariate quasi-copulas with quadratic sections in one variable. We also present and analyze examples to illustrate our results.
LA - eng
KW - 1-Lipschitz condition; copula; quasi-copula; quadratic sections
UR - http://eudml.org/doc/33971
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. Cuculescu I., Theodorescu R., Copulas: diagonals and tracks, Rev. Roumaine Math. Pures Appl. 46 (2001), 731–742 MR1929521
  3. Baets B. De, Meyer, H. De, Úbeda-Flores M., 10.1016/j.crma.2007.03.026, C. R. Acad. Sci. Paris, Ser. I 344 (2007), 587–590 Zbl1131.62044MR2323747DOI10.1016/j.crma.2007.03.026
  4. Baets B. De, Meyer H. De, Schuymer, B. De, Jenei S., 10.1007/s00355-006-0093-3, Soc. Choice Welf. 26 (2006), 217–238 Zbl1158.91338MR2226508DOI10.1007/s00355-006-0093-3
  5. Durante F., Quesada-Molina J. J., Úbeda-Flores M., 10.1016/j.ins.2007.07.019, Inform. Sci. 177 (2007), 5715–5724 Zbl1132.68761MR2362216DOI10.1016/j.ins.2007.07.019
  6. Genest C., Quesada-Molina J. J., Rodríguez-Lallena J.A., Sempi C., 10.1006/jmva.1998.1809, J. Multivariate Anal. 69 (1999), 193–205 (1999) Zbl0935.62059MR1703371DOI10.1006/jmva.1998.1809
  7. Janssens S., Baets, B. De, Meyer H. De, Bell-type inequalities for quasi-copulas, Fuzzy Sets Syst. 148 (2004), 263–278 Zbl1057.81011MR2100199
  8. Klement E. P., Kolesárová A., 1–Lipschitz aggregation operators, quasi-copulas and copulas with given diagonals, In: Soft Methodology and Random Information Systems (M. López-Díaz, M.A. Gil, P. Grzegorzewski, O. Hryniewicz, and J. Lawry, eds.), Advances in Soft Computing, Berlin 2004, pp. 205–211 Zbl1071.62048MR2118098
  9. Klement E. P., Kolesárová A., Extension to copulas and quasi-copulas as special 1-Lipschitz aggregation operators, Kybernetika 41 (2005), 329–348 MR2181422
  10. Klement E. P., Kolesárová A., 10.1007/s00605-007-0460-x, Monatsh. Math. 152 (2007), 151–167 Zbl1138.60016MR2346431DOI10.1007/s00605-007-0460-x
  11. Kolesárová A., 1-Lipschitz aggregation operators and quasi-copulas, Kybernetika 39 (2003), 615–629 MR2042344
  12. Nelsen R. B., An Introduction to Copulas, Second edition. Springer, New York 2006 Zbl1152.62030MR2197664
  13. Nelsen R. B., Úbeda-Flores M., 10.1016/j.crma.2005.09.026, C. R. Acad. Sci. Paris, Ser. I 341 (2005), 583–586 Zbl1076.62053MR2182439DOI10.1016/j.crma.2005.09.026
  14. Nelsen R. B., Quesada-Molina J. J., Rodríguez-Lallena J. A., Úbeda-Flores M., Multivariate Archimedean quasi-copulas, In: Distributions with Given Marginals and Statistical Modelling (C. Cuadras, J. Fortiana, and J. A. Rodríguez, eds.), Kluwer, Dordrecht 2002, pp. 179–185 Zbl1135.62338MR2058991
  15. Nelsen R. B., Quesada-Molina J. J., Rodríguez-Lallena J. A., Úbeda-Flores M., 10.1016/j.jmva.2003.09.002, J. Multivariate Anal. 90 (2004), 348–358 Zbl1057.62038MR2081783DOI10.1016/j.jmva.2003.09.002
  16. Nelsen R. B., Quesada-Molina J. J., Rodríguez-Lallena J. A., Úbeda-Flores M., 10.1016/j.insmatheco.2006.11.011, Insurance: Math. Econom. 42 (2008), 473–483 Zbl1152.60311MR2404309DOI10.1016/j.insmatheco.2006.11.011
  17. Nelsen R. B., Quesada-Molina J. J., Schweizer, B., Sempi C., Derivability of some operations on distribution functions, In: Distributions with Fixed Marginals and Related Topics (L. Rüschendorf, B. Schweizer, and M. D. Taylor, eds.), CA: IMS Lecture Notes – Monograph Series Number 28), Hayward 1996, pp. 233–243 (1996) MR1485535
  18. Quesada-Molina J. J., Rodríguez-Lallena J. A., 10.1080/10485259508832652, J. Nonparametr. Statist. 5 (1995), 323–337 (1995) Zbl0857.62060MR1379534DOI10.1080/10485259508832652
  19. Quesada-Molina J. J., Saminger-Platz, S., Sempi C., 10.1016/j.na.2007.11.021, Nonlinear Anal. 69 (2008), 4654–4673 Zbl1151.62044MR2467261DOI10.1016/j.na.2007.11.021
  20. Rodríguez-Lallena J. A., Úbeda-Flores M., Best-possible bounds on sets of multivariate distribution functions, Comm. Statist. Theory Methods 33 (2004), 805–820 Zbl1066.62056MR2042768
  21. Rodríguez-Lallena J. A., Úbeda-Flores M., Compatibility of three bivariate quasi-copulas: Applications to copulas, In: Soft Methodology and Random Information Systems (M. López-Díaz, M. A. Gil, P. Grzegorzewski, O. Hryniewicz, and J. Lawry, eds.), Advances in Soft Computing, Springer, Berlin 2004, pp. 173–180 Zbl1064.62060MR2118094
  22. Rodríguez-Lallena J. A., Úbeda-Flores M., Multivariate copulas with quadratic sections in one variable, To appear Zbl1197.62051MR2746580
  23. Rodríguez-Lallena J. A., Úbeda-Flores M., Some new characterizations and properties of quasi-copulas, To appear in Fuzzy Sets and Systems.doi: 10.1016/j.fss.2008.02.007 Zbl1175.62048MR2493270
  24. Saminger S., Baets, B. De, Meyer H. De, On the dominance relation between ordinal sums of conjunctors, Kybernetika 42 (2006), 337–350 MR2253393
  25. Sklar A., Fonctions de répartition à n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris 8 (1959), 229–231 (1959) MR0125600
  26. Sklar A., Random variables, joint distributions, and copulas, Kybernetika 9 (1973), 449–460 (1973) MR0345164
  27. Úbeda-Flores M., A new family of trivariate proper quasi-copulas, Kybernetika 43 (2007), 75–85 Zbl1131.62048MR2343332

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.