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Best-possible bounds on the set of copulas with given degree of non-exchangeability
journal contribution
posted on 2014-09-01, 00:00 authored by Gleb BeliakovGleb Beliakov, B De Baets, H De Meyer, R B Nelsen, M Úbeda-FloresWe establish best-possible bounds on the set of quasi-copulas with given degree of non-exchangeability. These bounds are shown to be best-possible bounds as well for the set of copulas with given degree of non-exchangeability, and, consequently, also on the set of bivariate distribution functions of continuous random variables with given margins and given degree of non-exchangeability. Non-exchangeability of a (quasi-)copula is measured in the sense of Nelsen, i.e.proportional to the maximal absolute difference between this (quasi-)copula and its transpose. © 2014 Elsevier Inc.
History
Journal
Journal of mathematical analysis and applicationsVolume
417Issue
1Pagination
451 - 468Publisher
Academic Press Inc.Location
San Diego, Calif.Publisher DOI
Link to full text
ISSN
0022-247XeISSN
1096-0813Language
engPublication classification
C1 Refereed article in a scholarly journalUsage metrics
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No categories selectedKeywords
best-possible boundscopulalipschitz conditionmeasure of non-exchangeabilityquasi-copulascience & technologyphysical sciencesmathematics, appliedmathematicsbivariate distribution-functionsquasi-copulasaggregation operatorsdiagnal sectionsrandom-variablesarchimax copulasconstructioninequalitiesassociation
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