| Title:
|
Non-exchangeable random variables, Archimax copulas and their fitting to real data (English) |
| Author:
|
Bacigál, Tomáš |
| Author:
|
Jágr, Vladimír |
| Author:
|
Mesiar, Radko |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
47 |
| Issue:
|
4 |
| Year:
|
2011 |
| Pages:
|
519-531 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Archimax copula |
| Keyword:
|
dependence function |
| Keyword:
|
generator |
| MSC:
|
62A10 |
| MSC:
|
93E12 |
| idZBL:
|
Zbl 1227.93120 |
| idMR:
|
MR2884858 |
| . |
| Date available:
|
2011-09-23T11:15:48Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141656 |
| . |
| Reference:
|
[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. |
| Reference:
|
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| Reference:
|
[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. Zbl 1189.26015, MR 2606816 |
| Reference:
|
[4] Durante, F., Mesiar, R.: $L^\infty $-measure of non-exchangeability for bivariate extreme value and Archimax copulas.J. Math. Anal. Appl. 369 (2010), 2, 610–615. Zbl 1191.62094, MR 2651706, 10.1016/j.jmaa.2010.04.005 |
| Reference:
|
[5] Genest, G., Favre, A.-C.: Everything you always wanted to know about copula modeling but were afraid to ask.J. Hydrolog. Engrg. 12 (2007), 4, 347–368. 10.1061/(ASCE)1084-0699(2007)12:4(347) |
| Reference:
|
[6] Genest, C., Rémillard, B.: Tests of independence or randomness based on the empirical copula process.Test 13 (2004), 335–369. MR 2154005, 10.1007/BF02595777 |
| Reference:
|
[7] Genest, C., Rémillard, B., Beaudoin, D.: Goodness-of-fit tests for copulas: A review and a power study.Insurance Math. Econom. 44 (2009), 199–213. Zbl 1161.91416, MR 2517885, 10.1016/j.insmatheco.2007.10.005 |
| Reference:
|
[8] Genest, C., Ghoudi, K., Rivest, L.-P.: A semi-parametric estimation procedure of dependence parameters in multivariate families of distributions.Biometrika 82 (1995), 543–552. MR 1366280, 10.1093/biomet/82.3.543 |
| Reference:
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[9] Genest, C., Ghoudi, K., Rivest, L.-P.: Discussion of the paper by Frees and Valdez (1998).North Amer. Act. J. 2 (1998), 143–149. MR 2011244 |
| Reference:
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| Reference:
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| Reference:
|
[12] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms.Kluwer, Dordrecht 2000. Zbl 1010.03046, MR 1790096 |
| Reference:
|
[13] Liebscher, E.: Construction of Asymmetric multivariate copulas.J. Multivariate Anal. 99 (2008), 10, 2234–2250. Zbl 1151.62043, MR 2463386, 10.1016/j.jmva.2008.02.025 |
| Reference:
|
[14] Mesiarová, A.: k-l$_p$-Lipschitz t-norms.Internat. J. Approx. Reasoning 46 (2007), 3, 596–604. Zbl 1189.03058, MR 2371644, 10.1016/j.ijar.2007.02.002 |
| Reference:
|
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| Reference:
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| Reference:
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[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. |
| Reference:
|
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