Comptes Rendus
no. 9
Probability Theory/Statistics
Extremes of the mass distribution associated with a trivariate quasi-copula
[Extrêmes de la distribution de masse associée à une quasi-copula dans un espace tridimensionnel]

Présenté par : Paul Deheuvels

Bernard De Baets1 ; Hans De Meyer2 ; Manuel Úbeda-Flores3
1 Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, B-9000, Gent, Belgium
2 Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 S9, B-9000, Gent, Belgium
3 Departamento de Estadística y Matemática Aplicada, Universidad de Almería, Carretera de Sacramento s/n, La Cañada de San Urbano, 04120 Almería, Spain
Comptes Rendus. Mathématique, Volume 344 (2007) no. 9, pp. 587-590.

Nous identifions les extrêmes de la distribution de masse associée à une quasi-copula dans un espace tridimensionnel. Les résultats sont comparés à ceux obtenus dans le cas bidimensionnel.

We identify the extremes of the mass distribution associated with a trivariate quasi-copula and compare our findings with the bivariate case.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.03.026
Bernard De Baets 1 ; Hans De Meyer 2 ; Manuel Úbeda-Flores 3

1 Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, B-9000, Gent, Belgium
2 Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 S9, B-9000, Gent, Belgium
3 Departamento de Estadística y Matemática Aplicada, Universidad de Almería, Carretera de Sacramento s/n, La Cañada de San Urbano, 04120 Almería, Spain 
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     title = {Extremes of the mass distribution associated with a trivariate quasi-copula},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {587--590},
     publisher = {Elsevier},
     volume = {344},
     number = {9},
     year = {2007},
     doi = {10.1016/j.crma.2007.03.026},
     language = {en},
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Bernard De Baets; Hans De Meyer; Manuel Úbeda-Flores. Extremes of the mass distribution associated with a trivariate quasi-copula. Comptes Rendus. Mathématique, Volume 344 (2007) no. 9, pp. 587-590. doi : 10.1016/j.crma.2007.03.026. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.03.026/

[1] C. Alsina; R.B. Nelsen; B. Schweizer On the characterization of a class of binary operations on distribution functions, Statist. Probab. Lett., Volume 17 (1993), pp. 85-89

[2] E. Chong; S. Zak An Introduction to Optimization, Wiley-Interscience Series in Discrete Mathematics and Optimization, Wiley, 2001 (Chapters 15–16)

[3] I. Cuculescu; R. Theodorescu Copulas: diagonals and tracks, Rev. Roumaine Math. Pures Appl., Volume 46 (2001), pp. 731-742

[4] R.B. Nelsen Copulas and quasi-copulas: an introduction to their properties and applications (E.P. Klement; R. Mesiar, eds.), Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms, Elsevier, Amsterdam, 2005, pp. 391-413

[5] R.B. Nelsen An Introduction to Copulas, Springer, New York, 2006

[6] R.B. Nelsen; J.J. Quesada-Molina; J.A. Rodríguez-Lallena; M. Úbeda-Flores Some new properties of quasi-copulas (C. Cuadras; J. Fortiana; J.A. Rodríguez-Lallena, eds.), Distributions with Given Marginals and Statistical Modelling, Kluwer Academic Publishers, Dordrecht, 2002, pp. 187-194

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