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The fundamental best-possible bounds inequality for bivariate distribution functions with given margins is the Fre´chet-Hoeffding inequality: If H denotes the joint distribution function of random variables X and Y whose margins are F and G; respectively, then maxð0; F ðxÞ þ GðyÞ À 1ÞpHðx; yÞpminðF ðxÞ; GðyÞÞ for all x; y in ½ÀN; N: In this paper we employ copulas and quasi-copulas to find similar best-possible bounds on arbitrary sets of bivariate distribution functions with given margins. As an application, we discuss bounds for a bivariate distribution function H with given margins F and G when the values of H are known at quartiles of X and Y : r

Blomqvist’s beta, copula, measures of multivariate association, Spearman’s footrule,

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