Geodesic
Lower cone distribution functions and set-valued quantiles form Galois connections
Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 2, pp. 221-236 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that a recently introduced lower cone distribution function, together with the set-valued multivariate quantile, generates a Galois connection between a complete lattice of closed convex sets and the interval $[0,1]$. This generalizes the corresponding univariate result. It is also shown that an extension of the lower cone distribution function and the set-valued quantile characterize the capacity functional of a random set extension of the original multivariate variable along with its distribution.
Mots-clés : Galois connection, multivariate quantile
Keywords: complete lattice, lower cone distribution function, random set. 
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C. Ararat; A. Hamel. Lower cone distribution functions and set-valued quantiles form Galois connections. Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 2, pp. 221-236. http://geodesic.mathdoc.fr/item/TVP_2020_65_2_a0/

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