| Title:
|
Generalized logistic model and its orthant tail dependence (English) |
| Author:
|
Ferreira, Helena |
| Author:
|
Pereira, Luisa |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
47 |
| Issue:
|
5 |
| Year:
|
2011 |
| Pages:
|
732-739 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The Multivariate Extreme Value distributions have shown their usefulness in environmental studies, financial and insurance mathematics. The Logistic or Gumbel-Hougaard distribution is one of the oldest multivariate extreme value models and it has been extended to asymmetric models. In this paper we introduce generalized logistic multivariate distributions. Our tools are mixtures of copulas and stable mixing variables, extending approaches in Tawn [14], Joe and Hu [6] and Fougères et al. [3]. The parametric family of multivariate extreme value distributions considered presents a flexible dependence structure and we compute for it the multivariate tail dependence coefficients considered in Li [7]. (English) |
| Keyword:
|
multivariate extreme value distribution |
| Keyword:
|
tail dependence |
| Keyword:
|
logistic model |
| Keyword:
|
mixture |
| MSC:
|
60G70 |
| idZBL:
|
Zbl 1250.62027 |
| idMR:
|
MR2850460 |
| . |
| Date available:
|
2011-11-10T15:40:07Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141688 |
| . |
| Reference:
|
[1] Capéraà, P., Fougères, A. L., Genest, C.: Bivariate distributions with given extreme value attractor.J. Multivariate Anal. 72 (2000), 30–49. MR 1747422, 10.1006/jmva.1999.1845 |
| Reference:
|
[2] Cuadras, C. M., Augé, J.: A continuous general multivariate distribution and its properties.Comm. Statist. A - Theory Methods 10 (1981), 339–353. MR 0612401, 10.1080/03610928108828042 |
| Reference:
|
[3] Fougères, A.-L., Nolan, J. P., Rootzén, H.: Models for dependent extremes using scale mixtures.Scand. J. Statist. 36 (2009), 42–59. MR 2508330 |
| Reference:
|
[4] Heffernan, J. E., Tawn, J. A., Zhang, Z.: Asymptotically (in)dependent multivariate maxima of moving maxima processes.Extremes 10 (2007), 57–82. MR 2397551, 10.1007/s10687-007-0035-1 |
| Reference:
|
[5] Joe, H.: Multivariate Models and Dependence Concepts.Chapman & Hall, London 1997. MR 1462613 |
| Reference:
|
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| Reference:
|
[7] Li, H.: Orthant tail dependence of multivariate extreme value distributions.J. Multivariate Anal. 100 (2009), 243–256. Zbl 1151.62041, MR 2460490, 10.1016/j.jmva.2008.04.007 |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
[13] Smith, R. L., Weissman, I.: Characterization and Estimation of the Multivariate Extremal Index.Technical Report, Univ. North Carolina 1996. |
| Reference:
|
[14] Tawn, J.: Modelling multivariate extreme value distributions.Biometrika 77 (1990), 2, 245–253. Zbl 0716.62051, 10.1093/biomet/77.2.245 |
| . |
