Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
Archimax copula; dependence function; generator
Archimax copula; dependence function; generator
Summary:
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.
References:
[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 10.1006/jmva.1999.1845 | MR 1747422
[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 2606816 | Zbl 1189.26015
[4] Durante, F., Mesiar, R.: $L^\infty $-measure of non-exchangeability for bivariate extreme value and Archimax copulas. J. Math. Anal. Appl. 369 (2010), 2, 610–615. DOI 10.1016/j.jmaa.2010.04.005 | MR 2651706 | Zbl 1191.62094
[5] Genest, G., Favre, A.-C.: Everything you always wanted to know about copula modeling but were afraid to ask. J. Hydrolog. Engrg. 12 (2007), 4, 347–368. DOI 10.1061/(ASCE)1084-0699(2007)12:4(347)
[6] Genest, C., Rémillard, B.: Tests of independence or randomness based on the empirical copula process. Test 13 (2004), 335–369. DOI 10.1007/BF02595777 | MR 2154005
[7] Genest, C., Rémillard, B., Beaudoin, D.: Goodness-of-fit tests for copulas: A review and a power study. Insurance Math. Econom. 44 (2009), 199–213. DOI 10.1016/j.insmatheco.2007.10.005 | MR 2517885 | Zbl 1161.91416
[8] Genest, C., Ghoudi, K., Rivest, L.-P.: A semi-parametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika 82 (1995), 543–552. DOI 10.1093/biomet/82.3.543 | MR 1366280
[9] Genest, C., Ghoudi, K., Rivest, L.-P.: Discussion of the paper by Frees and Valdez (1998). North Amer. Act. J. 2 (1998), 143–149. MR 2011244
[10] Joe, H.: Multivariate Models and Dependence Concepts. Chapman and Hall, London 1997. MR 1462613
[11] Khoudraji, A.: Contributions à l’étude des copules et à la modélisation des valeurs extrémes bivariées. PhD. Thesis, Université Laval, Québec 1995.
[12] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer, Dordrecht 2000. MR 1790096 | Zbl 1010.03046
[13] Liebscher, E.: Construction of Asymmetric multivariate copulas. J. Multivariate Anal. 99 (2008), 10, 2234–2250. DOI 10.1016/j.jmva.2008.02.025 | MR 2463386 | Zbl 1151.62043
[14] Mesiarová, A.: k-l$_p$-Lipschitz t-norms. Internat. J. Approx. Reasoning 46 (2007), 3, 596–604. DOI 10.1016/j.ijar.2007.02.002 | MR 2371644 | Zbl 1189.03058
[15] Nelsen, R. B.: An Introduction to Copulas. Second edition. Springer–Verlag, New York 2006. MR 2197664 | Zbl 1152.62030
[16] 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
[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 10.1016/0165-0114(80)90013-5 | MR 0589241 | Zbl 0443.04008
Search
Partner of
