zbMATH — the first resource for mathematics

Extreme value attractors for star unimodal copulas. (English) Zbl 0996.60026
This work examines the maximum domain of attraction for star unimodal copulas. For copulas that are star unimodal about \((a,b) \neq (1,1)\) the maximum domain is an element of a two-parameter family of copulas extending that of Cuadras-Auge. When \((a,b) = (1,1)\) the set of all possible attractors covers all maximum (extreme) values of star unimodality. Also, the archimax copulas of Ph. Capéraà, A.-L. Fougères and C. Genest [J. Multivariate Anal. 72, No. 1, 30-49 (2000; Zbl 0978.62043)] are studied. Many of the last copulas are not star unimodal.

60E99 Distribution theory
62H05 Characterization and structure theory for multivariate probability distributions; copulas
Full Text: DOI
[1] Bertin, E.; Cuculescu, I.; Theodorescu, R., Unimodality of probability measures, (1997), Kluwer Academic Dordrecht · Zbl 0876.60001
[2] Capéraà, P.; Fougères, A.-L.; Genest, C., Bivariate distributions with given extreme value attractor, J. multivariate anal., 72, 30-49, (2000) · Zbl 0978.62043
[3] I. Cuculescu, R. Theodorescu, Are copulas unimodal?, J. Multivariate Anal. (2002) (accepted with revision) · Zbl 1028.60009
[4] I. Cuculescu, R. Theodorescu, Unimodal copulas: maximum domain of attraction, Preprint nr. 01-02, University Laval, Department Math. Statist., 2001 · Zbl 1050.62060
[5] Dharmadhikari, S.W.; Joag-dev, K., Unimodality, convexity, and applications, (1988), Academic Press New York
[6] Galambos, J., The asymptotic theory of extreme order statistics, (1987), Krieger Malabar · Zbl 0634.62044
[7] Nelsen, R.B., An introduction to copulas, (1999), Springer New York · Zbl 0909.62052
[8] Pickands, J., Multivariate extreme value distributions, (), 859-878 · Zbl 0518.62045
[9] Sklar, A., Fonctions de répartition à n dimensions et leurs marges, Publ. inst. statist. univ. Paris, 8, 229-231, (1959) · Zbl 0100.14202
[10] Tawn, J.A., Bivariate extreme value theory: models and estimation, Biometrika, 75, 397-415, (1988) · Zbl 0653.62045
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.