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The Frank inequality
- 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.
- Subjects :
- Statistics::Theory
Mathematics::Dynamical Systems
Inequality
Logic
media_common.quotation_subject
Copula (linguistics)
Statistics::Other Statistics
02 engineering and technology
Unit square
01 natural sciences
Statistics::Computation
010104 statistics & probability
Artificial Intelligence
Frank copula
Idempotence
0202 electrical engineering, electronic engineering, information engineering
Calculus
Statistics::Methodology
020201 artificial intelligence & image processing
0101 mathematics
Mathematical economics
Random variable
Associative property
media_common
Mathematics
Subjects
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