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arXiv · 1812.06268

Lower cone distribution functions and set-valued quantiles form Galois connections

Cagin Ararat·Andreas H Hamel
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Abstract

It is shown that the recently introduced lower cone distribution function and the associated set-valued multivariate quantile generate a Galois connection between a complete lattice of closed convex sets and the intervall [0,1]. This generalizes the (not so well-known) 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.

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Cagin Ararat, Andreas H Hamel. 2018-12-15. Lower cone distribution functions and set-valued quantiles form Galois connections. https://doi.org/10.1137/s0040585x97t989908

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