no. 8
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.

Reçu le :
Révisé le :
Publié le :
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 
@article{CRMATH_2002__334_8_689_0,
     author = {Cuculescu, Ioan and Theodorescu, Radu},
     title = {Extreme value attractors for star unimodal copulas},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {689--692},
     publisher = {Elsevier},
     volume = {334},
     number = {8},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02322-1},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02322-1/}
}
TY  - JOUR
AU  - Cuculescu, Ioan
AU  - Theodorescu, Radu
TI  - Extreme value attractors for star unimodal copulas
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 689
EP  - 692
VL  - 334
IS  - 8
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/S1631-073X(02)02322-1/
DO  - 10.1016/S1631-073X(02)02322-1
LA  - en
ID  - CRMATH_2002__334_8_689_0
ER  - 
%0 Journal Article
%A Cuculescu, Ioan
%A Theodorescu, Radu
%T Extreme value attractors for star unimodal copulas
%J Comptes Rendus. Mathématique
%D 2002
%P 689-692
%V 334
%N 8
%I Elsevier
%U http://www.numdam.org/articles/10.1016/S1631-073X(02)02322-1/
%R 10.1016/S1631-073X(02)02322-1
%G en
%F CRMATH_2002__334_8_689_0
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/

[1] Bertin, E.; Cuculescu, I.; Theodorescu, R. Unimodality of Probability Measures, Kluwer Academic, Dordrecht, 1997

[2] Capéraà, P.; Fougères, A.-L.; Genest, C. Bivariate distributions with given extreme value attractor, J. Multivariate Anal., Volume 72 (2000), pp. 30-49

[3] I. Cuculescu, R. Theodorescu, Are copulas unimodal?, J. Multivariate Anal. (2002) (accepted with revision)

[4] I. Cuculescu, R. Theodorescu, Unimodal copulas: maximum domain of attraction, Preprint nr. 01-02, University Laval, Department Math. Statist., 2001

[5] Dharmadhikari, S.W.; Joag-dev, K. Unimodality, Convexity, and Applications, Academic Press, New York, 1988

[6] Galambos, J. The Asymptotic Theory of Extreme Order Statistics, Krieger, Malabar, 1987

[7] Nelsen, R.B. An Introduction to Copulas, Springer, New York, 1999

[8] Pickands, J. Multivariate extreme value distributions, Proc. 43rd Session Internat. Statist. Inst., Buenos Aires, 1981, pp. 859-878

[9] Sklar, A. Fonctions de répartition à n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris, Volume 8 (1959), pp. 229-231

[10] Tawn, J.A. Bivariate extreme value theory: Models and estimation, Biometrika, Volume 75 (1988), pp. 397-415

Cité par Sources :