Geodesic
A new family of trivariate proper quasi-copulas
Kybernetika, Tome 43 (2007) no. 1, pp. 75-85 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper, we provide a new family of trivariate proper quasi-copulas. As an application, we show that $W^{3}$ – the best-possible lower bound for the set of trivariate quasi-copulas (and copulas) – is the limit member of this family, showing how the mass of $W^3$ is distributed on the plane $x+y+z=2$ of $[0,1]^3$ in an easy manner, and providing the generalization of this result to $n$ dimensions.
In this paper, we provide a new family of trivariate proper quasi-copulas. As an application, we show that $W^{3}$ – the best-possible lower bound for the set of trivariate quasi-copulas (and copulas) – is the limit member of this family, showing how the mass of $W^3$ is distributed on the plane $x+y+z=2$ of $[0,1]^3$ in an easy manner, and providing the generalization of this result to $n$ dimensions.
Classification : 60E05, 62H05
Keywords: copula; mass distribution; quasi-copula 
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Úbeda-Flores, Manuel. A new family of trivariate proper quasi-copulas. Kybernetika, Tome 43 (2007) no. 1, pp. 75-85. http://geodesic.mathdoc.fr/item/KYB_2007_43_1_a5/

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