Geodesic
Non-exchangeable random variables, Archimax copulas and their fitting to real data
Kybernetika, Tome 47 (2011) no. 4, pp. 519-531
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The aim of this paper is to open a new way of modelling non-exchangeable random variables with a class of Archimax copulas. We investigate a connection between powers of generators and dependence functions, and propose some construction methods for dependence functions. Application to different hydrological data is given.
The aim of this paper is to open a new way of modelling non-exchangeable random variables with a class of Archimax copulas. We investigate a connection between powers of generators and dependence functions, and propose some construction methods for dependence functions. Application to different hydrological data is given.
Classification : 62A10, 93E12
Keywords: Archimax copula; dependence function; generator 
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Bacigál, Tomáš; Jágr, Vladimír; Mesiar, Radko. Non-exchangeable random variables, Archimax copulas and their fitting to real data. Kybernetika, Tome 47 (2011) no. 4, pp. 519-531. http://geodesic.mathdoc.fr/item/KYB_2011_47_4_a1/

[1] Bacigál, T., Juráňová, M., Mesiar, R.: On some new constructions of Archimedean copulas and applications to fitting problems. Neural Network World 1 (2010), 10, 81–90.

[2] Capéraá, P., Fougéres, A.-L., Genest, G.: Bivariate distributions with given extreme value attractor. J. Multivariate Anal. 72 (2000), 1, 30–49. | DOI | MR

[3] De Baets, B., De Meyer, H., Mesiar, R.: Lipschitz continuity of copulas w.r.t. $L_p$-norms. Nonlinear Anal., Theory, Methods Appl. 72(9-10) (2010), 3722–3731. | MR | Zbl

[4] Durante, F., Mesiar, R.: $L^\infty $-measure of non-exchangeability for bivariate extreme value and Archimax copulas. J. Math. Anal. Appl. 369 (2010), 2, 610–615. | DOI | MR | Zbl

[5] Genest, G., Favre, A.-C.: Everything you always wanted to know about copula modeling but were afraid to ask. J. Hydrolog. Engrg. 12 (2007), 4, 347–368. | DOI

[6] Genest, C., Rémillard, B.: Tests of independence or randomness based on the empirical copula process. Test 13 (2004), 335–369. | DOI | MR

[7] Genest, C., Rémillard, B., Beaudoin, D.: Goodness-of-fit tests for copulas: A review and a power study. Insurance Math. Econom. 44 (2009), 199–213. | DOI | MR | Zbl

[8] Genest, C., Ghoudi, K., Rivest, L.-P.: A semi-parametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika 82 (1995), 543–552. | DOI | MR

[9] Genest, C., Ghoudi, K., Rivest, L.-P.: Discussion of the paper by Frees and Valdez (1998). North Amer. Act. J. 2 (1998), 143–149. | MR

[10] Joe, H.: Multivariate Models and Dependence Concepts. Chapman and Hall, London 1997. | MR

[11] Khoudraji, A.: Contributions à l’étude des copules et à la modélisation des valeurs extrémes bivariées. PhD. Thesis, Université Laval, Québec 1995.

[12] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer, Dordrecht 2000. | MR | Zbl

[13] Liebscher, E.: Construction of Asymmetric multivariate copulas. J. Multivariate Anal. 99 (2008), 10, 2234–2250. | DOI | MR | Zbl

[14] Mesiarová, A.: k-l$_p$-Lipschitz t-norms. Internat. J. Approx. Reasoning 46 (2007), 3, 596–604. | DOI | MR | Zbl

[15] Nelsen, R. B.: An Introduction to Copulas. Second edition. Springer–Verlag, New York 2006. | MR | Zbl

[16] Tawn, J. A.: Bivariate extreme value theory: Models and estimation. Biometrika 75 (1988), 397–415. | DOI | MR | Zbl

[17] Vorosmarty, C. J., Fekete, B. M., A., B., Tucker: Global River Discharge, 1807-1991, V. 1.1 (RivDIS). Data set. 1998. Available on-line [ http://www.daac.ornl.gov] from Oak Ridge National Laboratory Distributed Active Archive Center, Oak Ridge, TN, U.S.A. doi:10.3334/ORNLDAAC/199.

[18] Yager, R. R.: On a general class of fuzzy connectives. Fuzzy Sets and Systems 4 (1980), 3, 235–242. | DOI | MR | Zbl