Geodesic
A note on biconic copulas
Kybernetika, Tome 47 (2011) no. 4, pp. 532-540 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We describe a class of bivariate copulas having a fixed diagonal section. The obtained class contains both the Fréchet upper and lower bounds and it allows to describe non-trivial tail dependence coefficients along both the diagonals of the unit square.
We describe a class of bivariate copulas having a fixed diagonal section. The obtained class contains both the Fréchet upper and lower bounds and it allows to describe non-trivial tail dependence coefficients along both the diagonals of the unit square.
Classification : 62E10
Keywords: copulas; diagonal section; probability mass distribution; tail dependence 
@article{KYB_2011_47_4_a2,
     author = {Durante, Fabrizio and Fern\'andez-S\'anchez, Juan},
     title = {A note on biconic copulas},
     journal = {Kybernetika},
     pages = {532--540},
     year = {2011},
     volume = {47},
     number = {4},
     mrnumber = {2884859},
     zbl = {1227.62036},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2011_47_4_a2/}
}
TY  - JOUR
AU  - Durante, Fabrizio
AU  - Fernández-Sánchez, Juan
TI  - A note on biconic copulas
JO  - Kybernetika
PY  - 2011
SP  - 532
EP  - 540
VL  - 47
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/KYB_2011_47_4_a2/
LA  - en
ID  - KYB_2011_47_4_a2
ER  - 
%0 Journal Article
%A Durante, Fabrizio
%A Fernández-Sánchez, Juan
%T A note on biconic copulas
%J Kybernetika
%D 2011
%P 532-540
%V 47
%N 4
%U http://geodesic.mathdoc.fr/item/KYB_2011_47_4_a2/
%G en
%F KYB_2011_47_4_a2
Durante, Fabrizio; Fernández-Sánchez, Juan. A note on biconic copulas. Kybernetika, Tome 47 (2011) no. 4, pp. 532-540. http://geodesic.mathdoc.fr/item/KYB_2011_47_4_a2/

[1] Baets, B. De, Meyer, H. De, Mesiar, R.: Asymmetric semilinear copulas. Kybernetika 43 (2007), 221–233. | MR | Zbl

[2] Baets, B. De, Meyer, H. De, Úbeda-Flores, M.: Opposite diagonal sections of quasi-copulas and copulas. Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 17 (2009), 481–490. | DOI | MR | Zbl

[3] Baets, B. De, Meyer, H. De, Úbeda-Flores, M.: Constructing copulas with given diagonal and opposite diagonal sections. Comm. Statist. Theory Methods 40 (2011), 828–843. | DOI | MR | Zbl

[4] Durante, F., Fernández-Sánchez, J.: On the classes of copulas and quasi-copulas with a given diagonal section. Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 19 (2011), 1–10. | DOI | MR | Zbl

[5] Durante, F., Jaworski, P.: A new characterization of bivariate copulas: Comm. Statist. Theory Methods 39 (2010), 2901–2912. | DOI | MR

[6] Durante, F., Kolesárová, A., Mesiar, R., Sempi, C.: Copulas with given diagonal sections: novel constructions and applications. Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 15 (2007), 397–410. | DOI | MR | Zbl

[7] Durante, F., Kolesárová, A., Mesiar, R., Sempi, C.: Semilinear copulas. Fuzzy Sets and Systems 159 (2008), 63–76. | MR

[8] Durante, F., Rodríguez-Lallena, J.A., Úbeda-Flores, M.: New constructions of diagonal patchwork copulas. Inform. Sci. 179 (2009), 3383–3391. | DOI | MR | Zbl

[9] Jaworski, P., Durante, F., Härdle, W., Rychlik, T.: Copula Theory and its Applications. Lecture Notes in Statist. - Proceedings 198. Springer, Berlin 2010. | Zbl

[10] Joe, H.: Multivariate Models and Dependence Concepts. Monographs Statist. Appl. Probab. 73. Chapman &Hall, London 1997. | MR | Zbl

[11] Jwaid, T., Baets, B. De: Double-conic copulas. In: Proc. FSTA 2010 (E. P. Klement et al., eds.), 2010, p. 73.

[12] Jwaid, T., Baets, B. De, Meyer, H. De: Orbital semilinear copulas. Kybernetika 45 (2009), 1012–1029. | MR | Zbl

[13] Jwaid, T., Baets, B. De, Meyer, H. De: Biconic aggregation functions. Inform. Sci., in press, 2011. | MR | Zbl

[14] Jwaid, T., Baets, B. De, Meyer, H. De: Biconic aggregation functions with a given diagonal and opposite diagonal section. In: Proc. 7th EUSFLAT Conference. In press, 2011. | MR

[15] Jwaid, T., Baets, B. De, Kalická, J., Mesiar, R.: Conic aggregation functions. Fuzzy Sets and Systems 167 (2011), 3–20. | MR | Zbl

[16] Klement, E. P., Kolesárová, A.: Intervals of 1-Lipschitz aggregation operators, quasi-copulas, and copulas with given affine section. Monatsh. Math. 152 (2007), 151–167. | DOI | MR | Zbl

[17] Klement, E. P., rová, A. Kolesá, Mesiar, R., Sempi, C.: Copulas constructed from horizontal sections. Comm. Statist. Theory Methods 36 (2007), 2901–2911. | DOI | MR

[18] Mai, J.-F.: Extendibility of Marshall–Olkin Distributions via Lévy Subordinators and an Application to Portfolio Credit Risk. PhD. Thesis, Technical University of Munich 2010.

[19] Mayor, G., Mesiar, R., Torrens, J.: On quasi-homogeneous copulas. Kybernetika 44 (2008), 745–756. | MR | Zbl

[20] Mesiar, R., Sarkoci, P.: Open problems posed at the Tenth International Conference on Fuzzy Set Theory and Applications (FSTA 2010, Liptovský Ján, Slovakia). Kybernetika 46 (2010), 585–599. | MR | Zbl

[21] Nelsen, R. B.: An Introduction to Copulas. Springer Series in Statistics. Second edition. Springer, New York 2006. | MR | Zbl

[22] Nelsen, R. B., Quesada-Molina, J. J., Rodríguez-Lallena, J. A., Úbeda-Flores, M.: On the construction of copulas and quasi-copulas with given diagonal sections. Insurance Math. Econom. 42 (2008), 473–483. | DOI | MR | Zbl

[23] Quesada-Molina, J. J., Saminger-Platz, S., Sempi, C.: Quasi-copulas with a given sub-diagonal section. Nonlinear Anal. 69 (2008), 4654–4673. | DOI | MR | Zbl

[24] Rodríguez-Lallena., J. A.: A class of copulas with piecewise linear horizontal sections. J. Statist. Plan. Infer. 139 (2009), 3908–3920. | DOI | MR | Zbl

[25] Úbeda-Flores, M.: Multivariate copulas with cubic sections in one variable. J. Nonparametr. Statist. 20 (2008), 91–98. | DOI | MR

[26] Yeh, J.: Lectures on Real Analysis. World Scientific Publishing Co. Inc., River Edge, NJ, 2000. | MR | Zbl

[27] Zhang, M.-H.: Modelling total tail dependence along diagonals. Insurance Math. Econom. 42 (2008), 73–80. | DOI | MR | Zbl