Comptes Rendus
no. 11-12
Probabilités
Comportement extrémal des copules diagonales et de Bertino
Christian Genest1 ; Magid Sabbagh2
1 Department of Mathematics and Statistics, McGill University, 805, rue Sherbrooke ouest, Montréal (Québec) Canada H3A 0B9
2 Department of Mathematics and Statistics, McGill University, 805, rue Sherbrooke ouest, Montréal (Québec) Canada H3A 0B9
Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1157-1167.

Les attracteurs maximaux des copules bivariées diagonales et de Bertino sont déterminés sous des conditions de régularité idoines. On en déduit des bornes sur l’attracteur maximal d’une copule symétrique à coupe diagonale donnée, ainsi que des bornes sur le rho de Spearman et le tau de Kendall d’une copule de valeurs extrêmes échangeable dont le coefficient de dépendance caudale supérieure est connu. Certains de ces résultats sont ensuite étendus aux cas de copules bivariées quelconques et de copules multivariées.

The maximal attractors of bivariate diagonal and Bertino copulas are determined under suitable regularity conditions. Some consequences of these facts are drawn, namely bounds on the maximal attractor of a symmetric copula with a given diagonal section, and bounds on Spearman’s rho and Kendall’s tau for an exchangeable extreme-value copula whose upper-tail dependence coefficient is known. Some of these results are then extended to the case of arbitrary bivariate copulas and to multivariate copulas.

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DOI : 10.5802/crmath.135
Classification : 60G70, 62G32
Christian Genest 1 ; Magid Sabbagh 2

1 Department of Mathematics and Statistics, McGill University, 805, rue Sherbrooke ouest, Montréal (Québec) Canada H3A 0B9
2 Department of Mathematics and Statistics, McGill University, 805, rue Sherbrooke ouest, Montréal (Québec) Canada H3A 0B9
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Christian Genest; Magid Sabbagh. Comportement extrémal des copules diagonales et de Bertino. Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1157-1167. doi : 10.5802/crmath.135. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.135/

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