Abstract
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 Manstavičius 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
