Authors: | Siburg, Karl F. Stoimenov, Pavel A. |
Title: | A scalar product for copulas |
Language (ISO): | en |
Abstract: | We 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. |
Subject Headings: | Copula Scalar product Sobolev space |
URI: | http://hdl.handle.net/2003/25270 http://dx.doi.org/10.17877/DE290R-8063 |
Issue Date: | 2008-05-15T09:16:00Z |
Appears in Collections: | Preprints der Fakultät für Mathematik |
Files in This Item:
File | Description | Size | Format | |
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mathematicalPreprint07.pdf | 331.08 kB | Adobe PDF | View/Open |
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