A characterization of quasi-copulas

The notion of quasi-copula was introduced by C. Alsina, R. B. Nelsen, and B . Schweizer (Statist. Probab. Lett. (1993), 85-89) and was used by these au thors and others to characterize operations on distribution functions that can or cannot be derived From operations on random variables. In this paper , the concept of quasi-copula is characterized in simpler operational terms and the result is used to show that absolutely continuous quasi-copulas ar e not necessarily copulas, thereby answering in the negative an open questi on of the above mentioned authors. (C) 1999 Academic Press. AMS 1991 subjec t classifications: 60E05, 62H05.