A scalar product for copulas

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dc.contributor.authorSiburg, Karl F.
dc.contributor.authorStoimenov, Pavel A.
dc.date.accessioned2008-05-15T09:16:00Z
dc.date.available2008-05-15T09:16:00Z
dc.date.issued2008-05-15T09:16:00Z
dc.description.abstractWe introduce a scalar product for n-dimensional copulas, based on the Sobolev scalar product for W^1,2-functions. The corresponding norm has quite remarkable properties and provides a new, geometric framework for copulas. We show that, in the bivariate case, it measures invertibility properties of copulas with respect to the *-operation introduced by Darsow et al. (1992). The unique copula of minimal norm is the null element for the *-operation, whereas the copulas of maximal norm are precisely the invertible elements.en
dc.identifier.urihttp://hdl.handle.net/2003/25270
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-8063
dc.language.isoende
dc.relation.ispartofseriesPreprints der Fakultät für Mathematik;2008-07de
dc.subjectCopulade
dc.subjectScalar producten
dc.subjectSobolev spaceen
dc.subject.ddc510
dc.titleA scalar product for copulasen
dc.typeTextde
dc.type.publicationtypepreprinten
dcterms.accessRightsopen access

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