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- W2247177458 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." @default.
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- W2247177458 date "2008-08-01" @default.
- W2247177458 modified "2023-09-26" @default.
- W2247177458 title "A scalar product for copulas" @default.
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- W2247177458 doi "https://doi.org/10.1016/j.jmaa.2008.02.045" @default.
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