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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TVP_2020_65_2_a0,
     author = {C. Ararat and A. Hamel},
     title = {Lower cone distribution functions and set-valued quantiles form {Galois} connections},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {221--236},
     publisher = {mathdoc},
     volume = {65},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2020_65_2_a0/}
}
TY  - JOUR
AU  - C. Ararat
AU  - A. Hamel
TI  - Lower cone distribution functions and set-valued quantiles form Galois connections
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2020
SP  - 221
EP  - 236
VL  - 65
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_2020_65_2_a0/
LA  - ru
ID  - TVP_2020_65_2_a0
ER  - 
%0 Journal Article
%A C. Ararat
%A A. Hamel
%T Lower cone distribution functions and set-valued quantiles form Galois connections
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2020
%P 221-236
%V 65
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_2020_65_2_a0/
%G ru
%F TVP_2020_65_2_a0
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/