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Article

Keywords:
copula; distortion; univariate conditioning; invariantness
Summary:
Based on a recent representation of copulas invariant under univariate conditioning, a new class of copulas linked to a distortion of the identity function is introduced and studied.
References:
[1] P. Capéraà, Fougères, A.-L., Genest, C.: Bivariate distributions with given extreme value attractor. J. Multivariate Anal. 72 (2000), 30–49 DOI 10.1006/jmva.1999.1845 | MR 1747422
[2] Baets, B. De, Meyer, H. De: Orthogonal grid constructions of copulas. IEEE Trans. Fuzzy Syst. 15 (2007), 6, 1053–1062. DOI 10.1109/TFUZZ.2006.890681
[3] Baets, B. De, Meyer, H. De, Kalická, J., Mesiar, R.: Flipping and cyclic shifting of binary aggragation functions. Fuzzy Sets and Systems 160 (2009), 6, 752–765. MR 2493273
[4] Durante, F., Jaworski, P.: Invariant dependence structure under univariate truncation. Statistics 2001, in press. MR 2903526
[5] Durante, F., Saminger-Platz, S., Sarkoci, P.: On patchwork techniques for $2$-increasing aggregation functions and copulas. In: Proc. SMPS, Toulouse 2008, pp. 349–356.
[6] Gudendorf, G., Segers, J.: Extreme-value copulas. In: Proc. Workshop on Copula Theory and Its Applications (P. Jaworski, F. Durante, W. Haerdle, T. Rychlik, eds.), Springer Media 2010, to appear.
[7] Jágr, V., Komorníková, M., Mesiar, R.: Conditioning stable copulas. Neural Netw. World 20 (2010), 1, 69–79.
[8] Joe, H.: Multivariate models and dependence concepts. Monographs Statist. Appl. Probab. 73, Chapman and Hall, London 1997. MR 1462613 | Zbl 0990.62517
[9] Khoudraji, A.: Contributions à l’étude des copules et à la modélisation des valeurs extrêmes bivariées. Ph.D. Thesis, Université Laval Québec 1995.
[10] Klement, E. P., Mesiar, R., Pap, E.: Quasi- and pseudo-inverses of monotone functions, and the construction of t-norms. Fuzzy Sets and Systems 104 (1999), 1, 3–13. DOI 10.1016/S0165-0114(98)00252-8 | MR 1685803 | Zbl 0953.26008
[11] Klement, E. P., Manzi, M., Mesiar, R.: Ultramodular aggregation functions and a new construction method for copulas. Submitted, 2010. MR 2818960
[12] Liebscher, E.: Construction of asymmetric multivariate copulas. J. Multivariate Analysis 99 (2008), 2234–2250. DOI 10.1016/j.jmva.2008.02.025 | MR 2463386 | Zbl 1151.62043
[13] Bacigál, T., Juráňová, M., Mesiar, R.: On some new constructions of Archimedean copulas and applications to fitting problems. Neural Network World 20 (2010), 81–90.
[14] Mesiar, R., Jágr, V., Juráňová, M., Komorníková, M.: Univariate conditioning of copulas. Kybernetika 44 (2009), 6, 807–816. MR 2488908
[15] Mesiar, R., Szolgay, J.: $W$-ordinals sum of copulas and quasi-copulas. In: Proc. MAGIA, Conference Kočovce 2004, pp. 78–83.
[16] Nelsen, R. B.: An Intorduction to Copulas. Springer Series in Statistics. Second edition. Springer, New York 2006. MR 2197664
[17] Rückschlossová, T., Rückschloss, R.: Homogeneous aggregation operators. Kybernetika 42 (2006), 3, 279–286. MR 2253389 | Zbl 1249.26024
[18] Sklar, A.: Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 1959, pp. 229-231. MR 0125600
[19] Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. North-Holland, 1983. MR 0790314 | Zbl 0546.60010
[20] Tawn, J. A.: Bivariate extreme value theory. Models and estimation. Biometrika 75 (1988), 397–415. DOI 10.1093/biomet/75.3.397 | MR 0967580 | Zbl 0653.62045
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