Search

It is well known that every bivariate copula induces a positive measure on the Borel σ -algebra on [ 0 , 1 ] 2 , but there exist bivariate quasi-copulas that do not induce a signed measure on the same σ -algebra. In this paper we show that a signed measure induced by a bivariate quasi-copula can always be expressed as an infinite combination of measures induced by copulas. With this we are able to give the first characterization of measure-inducing quasi-copulas in the bivariate setting. [ABSTRACT FROM AUTHOR]

Abstract: We show that there exist bivariate proper quasi-copulas that do not induce a doubly stochastic signed measure on . We construct these quasi-copulas from the so-called proper quasi-transformation square matrices. [Copyright &y& Elsevier]

Abstract: We study the relationship between multivariate quasi-copulas and measures that they may or may not induce on . We first study the mass distribution of the pointwise best possible lower bound for the set of n-quasi-copulas for . As a consequence, we show that not every n-quasi-copula induces a signed measure on . [Copyright &y& Elsevier]