The key role of convexity in some copula constructions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F20%3AA21025C1" target="_blank" >RIV/61988987:17610/20:A21025C1 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s40879-019-00346-3" target="_blank" >https://link.springer.com/article/10.1007/s40879-019-00346-3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s40879-019-00346-3" target="_blank" >10.1007/s40879-019-00346-3</a>

Result language
angličtina
Original language name
The key role of convexity in some copula constructions
Original language description
We start with some binary ('outer') copula, apply it to an arbitrary binary ('inner') copula and its dual (the latter being transformed by some real function) and ask under which conditions the result is again a binary copula. Sufficient convexity conditions for the transformation function and for the 'outer' copula (ultramodularity and Schur concavity) are given, thus generalizing the scenarios considered in Klement et al. (J Math Inequal 11(2):361-381, 2017) and Manstavicius and Bagdonas (Fuzzy Sets Syst 354:48-62, 2019). In general, these sufficient conditions are not necessary (and a counterexample is provided), but in some distinguished cases necessary and sufficient conditions can be given. Several well-known families of copulas can be obtained in this way. We also present a few extensions for special 'outer'/'inner' copulas and/or transformation functions, as well as some counterexamples.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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