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A characterization of quasi-copulas. (English) Zbl 0935.62059
A function $$Q:[0,1]^2\to[0,1]$$ is a quasi-copula if and only if it satisfies the three following conditions: (i) $$Q(0,x)=Q(x,0)=0$$, $$Q(x,1)=Q(1,x)=x$$, $$x\in[0,1]$$; (ii) $$Q(x,y)$$ is non-decreasing in each of its arguments; (iii) $$Q$$ satisfies a Lipschitz condition. The quasi-copula is comprised between the Fréchet bounds. The distinction between copulas and proper quasi-copulas is studied. Absolutely continuous quasi-copulas are not necessarily copulas.
Reviewer: P.Fronek (Praha)

##### MSC:
 62H05 Characterization and structure theory for multivariate probability distributions; copulas 60E05 Probability distributions: general theory
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