Generalized logistic model and its orthant tail dependence

Helena Ferreira; Luisa Pereira

Kybernetika (2011)

  • Volume: 47, Issue: 5, page 732-739
  • ISSN: 0023-5954

Abstract

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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].

How to cite

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Ferreira, Helena, and Pereira, Luisa. "Generalized logistic model and its orthant tail dependence." Kybernetika 47.5 (2011): 732-739. <http://eudml.org/doc/196606>.

@article{Ferreira2011,
abstract = {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].},
author = {Ferreira, Helena, Pereira, Luisa},
journal = {Kybernetika},
keywords = {multivariate extreme value distribution; tail dependence; logistic model; mixture; multivariate extreme value distributions; copulas; mixtures},
language = {eng},
number = {5},
pages = {732-739},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Generalized logistic model and its orthant tail dependence},
url = {http://eudml.org/doc/196606},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Ferreira, Helena
AU - Pereira, Luisa
TI - Generalized logistic model and its orthant tail dependence
JO - Kybernetika
PY - 2011
PB - Institute of Information Theory and Automation AS CR
VL - 47
IS - 5
SP - 732
EP - 739
AB - 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].
LA - eng
KW - multivariate extreme value distribution; tail dependence; logistic model; mixture; multivariate extreme value distributions; copulas; mixtures
UR - http://eudml.org/doc/196606
ER -

References

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  7. Li, H., 10.1016/j.jmva.2008.04.007, J. Multivariate Anal. 100 (2009), 243–256. (2009) Zbl1151.62041MR2460490DOI10.1016/j.jmva.2008.04.007
  8. Marshall, A. W., Olkin, I., 10.1080/01621459.1988.10478671, J. Amer. Statist. Assoc. 83 (1988), 834–841. (1988) Zbl0683.62029MR0963813DOI10.1080/01621459.1988.10478671
  9. McNeil, A. J., Frey, R., Embrechts, P., Quantitative Risk Management: Concepts, Techniques and Tools, Princeton University Press, Princeton 2005. (2005) Zbl1089.91037MR2175089
  10. Morillas, P. M., 10.1007/s001840400330, Metrika 61 (2005), 169–184. (2005) Zbl1079.62056MR2159414DOI10.1007/s001840400330
  11. Nelsen, R. B., An Introduction to Copulas, Springer, New York 1999. (1999) Zbl0909.62052MR1653203
  12. Schmid, F., Schmidt, R., 10.1016/j.jmva.2006.05.005, J. Multivariate Anal. 98 (2007), 1123–1140. (2007) Zbl1116.62061MR2326243DOI10.1016/j.jmva.2006.05.005
  13. Smith, R. L., Weissman, I., Characterization and Estimation of the Multivariate Extremal Index, Technical Report, Univ. North Carolina 1996. (1996) 
  14. Tawn, J., 10.1093/biomet/77.2.245, Biometrika 77 (1990), 2, 245–253. (1990) Zbl0716.62051DOI10.1093/biomet/77.2.245

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