Extreme Points of Polytopes of Discrete Copulas

DOI

10.2991/asum.k.210827.080How to use a DOI?

Keywords

Discrete Copulas, Transportation Polytopes, Extreme points

Abstract

Discrete copulas are useful tools in statistics to represent the joint distribution of discrete random vectors. Furthermore, they are fascinating mathematical objects that admit a representation as a convex polytope. In this work, we analyze the set of extreme points of convex polytopes of discrete copulas. We focus on the general class of discrete copulas defined on arbitrary grid domains of the unit square, thereby providing a complete characterization of extremal discrete copulas in the most general setting. To do so, we exploit well-known results on the extreme points of transportation polytopes. Finally, we show that the characterization presented here generalizes previous work on the topic.

Copyright

© 2021, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Elisa Perrone
AU  - Fabrizio Durante
PY  - 2021
DA  - 2021/08/30
TI  - Extreme Points of Polytopes of Discrete Copulas
BT  - Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)
PB  - Atlantis Press
SP  - 596
EP  - 601
SN  - 2589-6644
UR  - https://doi.org/10.2991/asum.k.210827.080
DO  - 10.2991/asum.k.210827.080
ID  - Perrone2021
ER  -