Best-possible bounds on the sets of copulas and quasi-copulas with given curvilinear sections

In this paper, we consider the (quasi-)copulas with a given curvilinear section, and then establish the best-possible bounds on the set of quasi-copulas with a common curvilinear section. The lower bound is shown to be the best-possible lower bound as well for the set of copulas with the given curvi...

Full description

Saved in:
Bibliographic Details
Published in:Fuzzy sets and systems 2022-08, Vol.441, p.335-365
Main Authors: Zou, Wei, Sun, Liulei, Xie, Jiehua
Format: Article
Language:English
Subjects:
Best-possible bound
Copula
Curvilinear section
Quasi-copula
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we consider the (quasi-)copulas with a given curvilinear section, and then establish the best-possible bounds on the set of quasi-copulas with a common curvilinear section. The lower bound is shown to be the best-possible lower bound as well for the set of copulas with the given curvilinear section. A sufficient and necessary condition guaranteeing the upper bound to be a copula is provided, and it is shown that when the upper bound is a copula, it is the best-possible upper bound for the set of copulas with the given curvilinear section. The best-possible upper bound on the set of copulas which have a common curvilinear section and are symmetrical with respect to the given curve is also provided. Some properties of the best-possible bound copulas with the given curvilinear section are also discussed, such as the statistical characteristic, the concordance order, the nonparametric measure of association and the tail dependence.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2021.12.008