A note on an idempotent transformation of absolutely continuous Archimedean copulas

In De Baets et al. [6] the authors define, for a copula C, an idempotent transformation D[C] which, in some cases, generates new copulas. In this note we give a (negative) answer to a question posed in [6], showing that D[C] is not necessarily a copula when C is an absolutely continuous Archimedean...

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Bibliographic Details
Published in:Fuzzy sets and systems 2020-08, Vol.393, p.160-166
Main Authors: Fernández-Sánchez, Juan, Úbeda-Flores, Manuel
Format: Article
Language:English
Subjects:
Archimedean copula
Copula
Idempotent transformation
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Summary:In De Baets et al. [6] the authors define, for a copula C, an idempotent transformation D[C] which, in some cases, generates new copulas. In this note we give a (negative) answer to a question posed in [6], showing that D[C] is not necessarily a copula when C is an absolutely continuous Archimedean copula.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2019.04.023