Extreme value attractors for star unimodal copulas

Ioan Cuculescu; Radu Theodorescu

doi:10.1016/S1631-073X(02)02322-1

Extreme value attractors for star unimodal copulas
[Attracteurs de valeurs extrêmes pour les copules 2-unimodales]

Ioan Cuculescu ¹ ; Radu Theodorescu ²

¹ Facultatea de matematică, Universitatea Bucureşti, str. Academiei 14, RO-70109 Bucureşti, Romania
² Département de mathématiques et de statistique, Université Laval, Québec, QC, Canada G1K 7P4

Comptes Rendus. Mathématique, Volume 334 (2002) no. 8, pp. 689-692.

Résumé
Abstract

Nous déterminons les attracteurs des valeurs maximales pour les copules 2-unimodales (par rapport à (a,b)). Si (a,b)≠(1,1) ces attracteurs forment une famille de copules à deux paramètres généralisant celle de Cuadras–Augé alors que si (a,b)=(1,1) elles couvrent toutes les copules de valeurs maximales. Nous examinons aussi la relation entre l'unimodalité et les copules Archimax.

We determine maximum attractors for copulas star (or 2-) unimodal (about a point $(a, b) \in R^{2}$ ). If (a,b)≠(1,1) these attractors form a two-parameter family of copulas extending that of Cuadras–Augé, whereas if (a,b)=(1,1) they cover all maximum value copulas. We also examine the relationship between unimodality and Archimax copulas.

Reçu le : 2001-12-05
Révisé le : 2002-02-18
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02322-1

Affiliations des auteurs :

Ioan Cuculescu ¹ ; Radu Theodorescu ²

¹ Facultatea de matematică, Universitatea Bucureşti, str. Academiei 14, RO-70109 Bucureşti, Romania
² Département de mathématiques et de statistique, Université Laval, Québec, QC, Canada G1K 7P4

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     title = {Extreme value attractors for star unimodal copulas},
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     language = {en},
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Ioan Cuculescu; Radu Theodorescu. Extreme value attractors for star unimodal copulas. Comptes Rendus. Mathématique, Volume 334 (2002) no. 8, pp. 689-692. doi : 10.1016/S1631-073X(02)02322-1. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02322-1/

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