an:01310064
Zbl 0935.62059
Genest, C.; Quesada Molina, J. J.; Rodr??guez Lallena, J. A.; Sempi, C.
A characterization of quasi-copulas
EN
J. Multivariate Anal. 69, No. 2, 193-205 (1999).
00056481
1999
j
62H05 60E05
uniform marginals Frechet bounds; Lipschitz condition; copulas; quasi-copulas
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 Fr??chet bounds. The distinction between copulas and proper quasi-copulas is studied. Absolutely continuous quasi-copulas are not necessarily copulas.
P.Fronek (Praha)