Abstract
We extend and sharpen some results in the literature concerning the notion of Markov product idempotence in some well-known classes of copulas. Focusing on families of copulas which are characterized by univariate functions we show that in the class of extreme-value copulas, in the class of diagonal copulas and in some special class of copulas represented by measure-preserving transformations only the usual suspects (if contained in the class) are idempotent, namely the product copula Π and minimum copula M. Additionally, we prove a conjecture going back to Albanese and Sempi in 2016 saying that the only idempotent Archimedean copula is the product copula Π.
Original language | English |
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Article number | 125184 |
Number of pages | 15 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 501 |
Issue number | 2 |
DOIs | |
Publication status | Published - 15 Sept 2021 |
Bibliographical note
Publisher Copyright:© 2021 The Author(s)
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
Keywords
- Copula
- Invariance
- Markov product
- Star product
Fields of Science and Technology Classification 2012
- 101 Mathematics