A characterization of quasi-copulas. (English) Zbl 0935.62059

Genest, C.; Quesada Molina, J. J.; Rodríguez Lallena, J. A.; Sempi, C.

J. Multivariate Anal. 69, No. 2, 193-205 (1999).

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

Keywords:

uniform marginals Frechet bounds; Lipschitz condition; copulas; quasi-copulas

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