Bivariate copulas, norms and non-exchangeability

• Autorzy: Pier Luigi Papini
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Copulas; Asymmetry; Measure of nonexchangeability

Kategorie tematyczne

• 62H20: Measures of association (correlation, canonical correlation, etc.)
• 60G09: Exchangeability
• 60E05: Distributions: general theory

• Wydawca: De Gruyter Open
• Czasopismo: Dependence Modeling
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-08-03

zaakceptowano

2015-10-23

online

2015-11-03

Twórcy

autor

Pier Luigi Papini

• Via Martucci, 19, 40136 Bologna, Italy

Bibliografia

• [1] E. Alvoni and P.L. Papini (2007). Quasi-concave copulas, asymmetry and transformations. Comment. Math. Univ. Carolin. 48(2), 311-319.
• [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] 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]
• [4] F. W. Darsow and E. T. Olsen (1995). Norms for copulas. Internat. J. Math. Math. Sci. 18(3), 417-436. [Crossref]
• [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]
• [6] F. Durante and P.L. Papini (2010). Non-exchangeability of negatively dependent random variables. Metrika 71(2), 139-149. [Crossref][WoS]
• [7] F. Durante and C. Sempi (2015). Principles of Copula Theory. Chapman & Hall/CRC, Boca Raton FL.
• [8] S. Fuchs and K.D. Schmidt (2014). Bivariate copulas: transformations, asymmetry and measures of concordance. Kybernetika 50(1), 109-125.
• [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.
• [10] E. P. Klement and R. Mesiar (2006). How non-symmetric can a copula be? Comment. Math. Univ. Carolin. 47(1), 141-148.
• [11] R. B. Nelsen (2006). An introduction to Copulas. Second Edition. Springer, New York.
• [12] R.B. Nelsen (2007). Extremes of nonexchangeability. Statist. Papers 48(2), 329-336. [Crossref]
• [13] K. F. Siburg and P. A. Stoimenov (2008). A scalar product for copulas. J. Math. Anal. Appl. 344(1), 429-439.
• [14] K. F. Siburg and P.A. Stoimenov (2011). Symmetry of functions and exchangeability of random variables. Statist. Papers 52(1), 1-15. [Crossref]

Identyfikatory

DOI

10.1515/demo-2015-0014