On quasi-homogeneous copulas

Gaspar Mayor; Radko Mesiar; Joan Torrens

Kybernetika (2008)

  • Volume: 44, Issue: 6, page 745-756
  • ISSN: 0023-5954

Abstract

top
Quasi-homogeneity of copulas is introduced and studied. Quasi-homogeneous copulas are characterized by the convexity and strict monotonicity of their diagonal sections. As a by-product, a new construction method for copulas when only their diagonal section is known is given.

How to cite

top

Mayor, Gaspar, Mesiar, Radko, and Torrens, Joan. "On quasi-homogeneous copulas." Kybernetika 44.6 (2008): 745-756. <http://eudml.org/doc/33962>.

@article{Mayor2008,
abstract = {Quasi-homogeneity of copulas is introduced and studied. Quasi-homogeneous copulas are characterized by the convexity and strict monotonicity of their diagonal sections. As a by-product, a new construction method for copulas when only their diagonal section is known is given.},
author = {Mayor, Gaspar, Mesiar, Radko, Torrens, Joan},
journal = {Kybernetika},
keywords = {copula; diagonal section; quasi-homogeneity; diagonal section; quasi-homogeneity},
language = {eng},
number = {6},
pages = {745-756},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On quasi-homogeneous copulas},
url = {http://eudml.org/doc/33962},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Mayor, Gaspar
AU - Mesiar, Radko
AU - Torrens, Joan
TI - On quasi-homogeneous copulas
JO - Kybernetika
PY - 2008
PB - Institute of Information Theory and Automation AS CR
VL - 44
IS - 6
SP - 745
EP - 756
AB - Quasi-homogeneity of copulas is introduced and studied. Quasi-homogeneous copulas are characterized by the convexity and strict monotonicity of their diagonal sections. As a by-product, a new construction method for copulas when only their diagonal section is known is given.
LA - eng
KW - copula; diagonal section; quasi-homogeneity; diagonal section; quasi-homogeneity
UR - http://eudml.org/doc/33962
ER -

References

top
  1. Aczél J., Lectures on Functional Equations and Their Applications (Math, Sci. Engrg., Vol. 19). Academic Press, New York 1966 (19).) MR0208210
  2. Alsina C., Frank M. J., Schweizer B., Associative Functions, Triangular Norms and Copulas. World Scientific Publishing, Singapore 2006 Zbl1100.39023MR2222258
  3. Bertino S., Sulla dissomiglianza tra mutabili cicliche, Metron 35 (1977), 53–88 (1977) Zbl0437.62026
  4. Baets B. De, Meyer, H. De, Mesiar R., Asymmetric semilinear copulas, Kybernetika 43 (2007), 221–233 Zbl1136.62350MR2343397
  5. Durante F., Kolesárová A., Mesiar, R., Sempi C., 10.1142/S0218488507004753, Internat. J. Uncertainty, Fuzziness and Knowledge-Based Systems 15 (2007), 397–410 Zbl1158.62324MR2362234DOI10.1142/S0218488507004753
  6. Durante F., Kolesárová A., Mesiar, R., Sempi C., Semilinear copulas, Fuzzy Sets and Systems 159 (2008), 63–76 MR2371303
  7. Durante F., Mesiar, R., Sempi C., 10.1007/s00500-005-0523-7, Soft Computing 10 (2006), 490–494 Zbl1098.60016DOI10.1007/s00500-005-0523-7
  8. Durante F., Sempi C., Semicopulae, Kybernetika 41 (2005), 315–328 MR2181421
  9. Ebanks B. R., 10.1155/S0161171298000489, Internat. J. Math. Math. Sci. 21 (1998), 351–358 (1998) Zbl0899.39003MR1609715DOI10.1155/S0161171298000489
  10. 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 1977, pp. 129–136 (1977) MR1614666
  11. 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, Dordrecht 2002, pp. 81–91 Zbl1135.62334MR2058982
  12. 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
  13. Klement E. P., Kolesárová A., Extension to copulas and quasi-copulas as special 1-Lipschitz aggregation operators, Kybernetika 41 (2005), 329–348 MR2181422
  14. Klement E. P., Mesiar, R., Pap E., Triangular Norms, Kluwer Academic Publishers, Dordrecht 2000 Zbl1087.20041MR1790096
  15. Nelsen R. B., An Introduction to Copulas, Second edition (Springer Series in Statistics). Springer-Verlag, New York 2006 Zbl1152.62030MR2197664

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.