Some New Properties of Quasi-Copulas

Abstract The notion of a quasi-copula was introduced by Alsina et al. (1993) to characterize operations on distribution functions that can or cannot be derived from operations on random variables. Genest et al. (1999) characterize the quasi-copula concept in simpler operational terms. We present a new simple characterization and some properties of these functions, all of them concerning the mass distribution of a quasi-copula. We show that the features of this mass distribution can be quite different from that of a copula.