Extreme value attractors for star unimodal copulas
[Attracteurs de valeurs extrêmes pour les copules 2-unimodales]
Cuculescu, Ioan1 ; Theodorescu, Radu2
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, Tome 334 (2002) no. 8, pp. 689-692.

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)∈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.

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DOI : 10.1016/S1631-073X(02)02322-1
Cuculescu, Ioan 1 ; Theodorescu, Radu 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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Cuculescu, Ioan; Theodorescu, Radu. Extreme value attractors for star unimodal copulas. Comptes Rendus. Mathématique, Tome 334 (2002) no. 8, pp. 689-692. doi : 10.1016/S1631-073X(02)02322-1. http://www.numdam.org/articles/10.1016/S1631-073X(02)02322-1/

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