zbMATH — the first resource for mathematics

Generalized logistic models and its orthant tail dependence. (English) Zbl 1250.62027
This paper introduces multivariate generalized logistic distributions as a subfamily of multivariate max-stable distributions. It contains many examples from the literature. The orthant tail dependence coefficient is computed and illustrated by examples.

62H10 Multivariate distribution of statistics
62G32 Statistics of extreme values; tail inference
62H05 Characterization and structure theory for multivariate probability distributions; copulas
Full Text: Link EuDML arXiv
[1] Capéraà, P., Fougères, A. L., Genest, C.: Bivariate distributions with given extreme value attractor. J. Multivariate Anal. 72 (2000), 30-49. · Zbl 0978.62043 · doi:10.1006/jmva.1999.1845
[2] Cuadras, C. M., Augé, J.: A continuous general multivariate distribution and its properties. Comm. Statist. A - Theory Methods 10 (1981), 339-353. · Zbl 0456.62013 · doi:10.1080/03610928108828042
[3] Fougères, A.-L., Nolan, J. P., Rootzén, H.: Models for dependent extremes using scale mixtures. Scand. J. Statist. 36 (2009), 42-59. · Zbl 1195.62067
[4] Heffernan, J. E., Tawn, J. A., Zhang, Z.: Asymptotically (in)dependent multivariate maxima of moving maxima processes. Extremes 10 (2007), 57-82. · Zbl 1150.60030 · doi:10.1007/s10687-007-0035-1
[5] Joe, H.: Multivariate Models and Dependence Concepts. Chapman & Hall, London 1997. · Zbl 0990.62517
[6] Joe, H., Hu, T.: Multivariate distributions from mixtures of max-infinitely divisible distributions. J. Multivariate Anal. 57 (1996), 240-265. · Zbl 0863.62047 · doi:10.1006/jmva.1996.0032
[7] Li, H.: Orthant tail dependence of multivariate extreme value distributions. J. Multivariate Anal. 100 (2009), 243-256. · Zbl 1151.62041 · doi:10.1016/j.jmva.2008.04.007
[8] Marshall, A. W., Olkin, I.: Families of multivariate distributions. J. Amer. Statist. Assoc. 83 (1988), 834-841. · Zbl 0683.62029 · doi:10.2307/2289314
[9] McNeil, A. J., Frey, R., Embrechts, P.: Quantitative Risk Management: Concepts, Techniques and Tools. Princeton University Press, Princeton 2005. · Zbl 1089.91037
[10] Morillas, P. M.: A method to obtain new copulas from a given one. Metrika 61 (2005), 169-184. · Zbl 1079.62056 · doi:10.1007/s001840400330
[11] Nelsen, R. B.: An Introduction to Copulas. Springer, New York 1999. · Zbl 0909.62052
[12] Schmid, F., Schmidt, R.: Multivariate conditional versions of Spearman’s rho and related measures of tail dependence. J. Multivariate Anal. 98 (2007), 1123-1140. · Zbl 1116.62061 · doi:10.1016/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.
[14] Tawn, J.: Modelling multivariate extreme value distributions. Biometrika 77 (1990), 2, 245-253. · Zbl 0716.62051 · doi:10.1093/biomet/77.2.245
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.