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Nelsen, Roger B; Molina, José Juan Quesada; Lallena, José Antonio Rodrı́guez; Flores, Manuel Úbeda
Journal of multivariate analysis, 08/2004, Letnik: 90, Številka: 2Journal Article
The fundamental best-possible bounds inequality for bivariate distribution functions with given margins is the Fréchet–Hoeffding inequality: If H denotes the joint distribution function of random variables X and Y whose margins are F and G, respectively, then max(0, F( x)+ G( y)−1)⩽ H( x, y)⩽min( F( x), G( y)) for all x, y in −∞,∞. 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.
