Bivariate copulas, norms and non-exchangeability

Pier Luigi Papini

Dependence Modeling (2015)

  • Volume: 3, Issue: 1, page 196-202, electronic only
  • ISSN: 2300-2298

Abstract

top
The present paper is related to the study of asymmetry for copulas by introducing functionals based on different norms for continuous variables. In particular, we discuss some facts concerning asymmetry and we point out some flaws occurring in the recent literature dealing with this matter.

How to cite

top

Pier Luigi Papini. "Bivariate copulas, norms and non-exchangeability." Dependence Modeling 3.1 (2015): 196-202, electronic only. <http://eudml.org/doc/275866>.

@article{PierLuigiPapini2015,
abstract = {The present paper is related to the study of asymmetry for copulas by introducing functionals based on different norms for continuous variables. In particular, we discuss some facts concerning asymmetry and we point out some flaws occurring in the recent literature dealing with this matter.},
author = {Pier Luigi Papini},
journal = {Dependence Modeling},
keywords = {Copulas; Asymmetry; Measure of nonexchangeability; copulas; asymmetry; measure of nonexchangeability},
language = {eng},
number = {1},
pages = {196-202, electronic only},
title = {Bivariate copulas, norms and non-exchangeability},
url = {http://eudml.org/doc/275866},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Pier Luigi Papini
TI - Bivariate copulas, norms and non-exchangeability
JO - Dependence Modeling
PY - 2015
VL - 3
IS - 1
SP - 196
EP - 202, electronic only
AB - The present paper is related to the study of asymmetry for copulas by introducing functionals based on different norms for continuous variables. In particular, we discuss some facts concerning asymmetry and we point out some flaws occurring in the recent literature dealing with this matter.
LA - eng
KW - Copulas; Asymmetry; Measure of nonexchangeability; copulas; asymmetry; measure of nonexchangeability
UR - http://eudml.org/doc/275866
ER -

References

top
  1. [1] E. Alvoni and P.L. Papini (2007). Quasi-concave copulas, asymmetry and transformations. Comment. Math. Univ. Carolin. 48(2), 311-319. Zbl1195.62074
  2. [2] E. Alvoni, F. Durante, P. L. Papini and C. Sempi (2007). Different types of convexity and concavity for copulas. In M. Stepnicka, V. Nowak and U. Bodenhofer (ed.s), Proc. 5th EUSFLAT Conf. Volume 1, Univ. Ostravensis, 185-189. 
  3. [3] G. Beliakov, B.De Baets, H. De Meyer, R.B. Nelsen and M. Úbeda-Flores (2014). Best possible bounds on the set of copulas with given degree of non-exchangeability. J. Math. Anal. Appl. 417(1), 451-468. [WoS] Zbl1308.62108
  4. [4] F. W. Darsow and E. T. Olsen (1995). Norms for copulas. Internat. J. Math. Math. Sci. 18(3), 417-436. [Crossref] Zbl0827.46011
  5. [5] F. Durante, E. P. Klement, C. Sempi and M. Úbeda-Flores (2010). Measures of non-exchangeability for bivariate random vectors. Statist. Papers 51(3), 687-699. [Crossref] Zbl1247.60047
  6. [6] F. Durante and P.L. Papini (2010). Non-exchangeability of negatively dependent random variables. Metrika 71(2), 139-149. [Crossref][WoS] Zbl1182.62119
  7. [7] F. Durante and C. Sempi (2015). Principles of Copula Theory. Chapman & Hall/CRC, Boca Raton FL. Zbl06445037
  8. [8] S. Fuchs and K.D. Schmidt (2014). Bivariate copulas: transformations, asymmetry and measures of concordance. Kybernetika 50(1), 109-125. Zbl06296994
  9. [9] C. Genest and J.G. Nešlehová (2013). Assessing and Modeling Asymmetry in Bivariate Continuous Data. In P. Jaworski, F. Durante and W.K. Härdle (ed.s), Copulae in Mathematical and Quantitative Finance, Springer Berlin. Zbl1273.62112
  10. [10] E. P. Klement and R. Mesiar (2006). How non-symmetric can a copula be? Comment. Math. Univ. Carolin. 47(1), 141-148. Zbl1150.62027
  11. [11] R. B. Nelsen (2006). An introduction to Copulas. Second Edition. Springer, New York. Zbl1152.62030
  12. [12] R.B. Nelsen (2007). Extremes of nonexchangeability. Statist. Papers 48(2), 329-336. [Crossref] Zbl1110.62071
  13. [13] K. F. Siburg and P. A. Stoimenov (2008). A scalar product for copulas. J. Math. Anal. Appl. 344(1), 429-439. Zbl1151.46023
  14. [14] K. F. Siburg and P.A. Stoimenov (2011). Symmetry of functions and exchangeability of random variables. Statist. Papers 52(1), 1-15. [Crossref] Zbl1247.60021

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.