Name
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. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.fss.2017.03.017 | Fuzzy Sets and Systems |
Keywords | DocType | Volume |
Associative copula,Frank copula,Frank equation,Frank inequality,Super-additivity,Radial symmetry | Journal | 335 |
ISSN | Citations | PageRank |
0165-0114 | 0 | 0.34 |
References | Authors | |
0 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bernard De Baets | 1 | 2994 | 300.39 |
| Hans De Meyer | 2 | 305 | 42.39 |