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The Frank inequality

Authors :
B. De Baets
H. De Meyer
Source :
Fuzzy Sets and Systems. 335:18-29
Publication Year :
2018
Publisher :
Elsevier BV, 2018.

Abstract

We investigate a functional inequality for copulas that has emerged from our study of the comparison of a set of random variables pairwisely coupled by a same copula. Any copula satisfying this inequality is necessarily symmetric and radially symmetric. Moreover, any associative copula satisfying this inequality is a solution to the well-known Frank equation. For this reason, the inequality is coined the Frank inequality. We fully characterize the associative copulas that satisfy the Frank inequality: they turn out to be either Frank copulas or ordinal sums of a same Frank copula with equidistant idempotent elements. As a by-product, we observe that Frank copulas are super-additive on the unit square.

Details

ISSN :
01650114
Volume :
335
Database :
OpenAIRE
Journal :
Fuzzy Sets and Systems
Accession number :
edsair.doi...........9354f8a8a400098a1b6862d9f18f67f8
Full Text :
https://doi.org/10.1016/j.fss.2017.03.017