A note on the copulas invariant with respect to \((a,b)\)-transformation. (English) Zbl 1464.62283
Summary: This paper answers the problem of copulas invariant with respect to \((a, b)\)-transformations recently proposed by Horanská and A. Kolesárová [Fuzzy Sets Syst. 326, 89–105 (2017; Zbl 1382.28011)]. Using tools from ergodic theory and iterated function systems we prove that the conjecture formulated therein is not true in general and for every \((a, b) \in\,]0, 1[^2\) we construct a one-parametric class of nontrivial copulas invariant with respect to \((a, b)\)-transformation.
MSC:
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
Citations:
Zbl 1382.28011References:
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