Some new properties of quasi-copulas. (English) Zbl 1135.62339

Cuadras, Carles M. (ed.) et al., Distributions with given marginals and statistical modelling. Papers presented at the meeting, Barcelona, Spain, July 17–20, 2000. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-0914-3/hbk). 187-194 (2002).
Summary: The notion of a quasi-copula was introduced by C. Alsina et al. [Stat. Probab. Lett. 17, No. 2, 85–89 (1993; Zbl 0798.60023)] to characterize operations on distribution functions that can or cannot be derived from operations on random variables. C. Genest et al. [J. Multivariate Anal. 69, No. 2, 193–205 (1999; Zbl 0935.62059)] 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 quasi-copulas. We show that the features of this mass distribution can be quite different from that of a copula.
For the entire collection see [Zbl 1054.62002].


62H05 Characterization and structure theory for multivariate probability distributions; copulas
60E05 Probability distributions: general theory
62E17 Approximations to statistical distributions (nonasymptotic)