Best-possible bounds on sets of bivariate distribution functions

Roger B. Nelsen, José Juan Quesada Molina, José Antonio Rodríguez Lallena and Manuel Úbeda Flores

Journal of Multivariate Analysis, 2004, vol. 90, issue 2, 348-358

Abstract: The fundamental best-possible bounds inequality for bivariate distribution functions with given margins is the Frechet-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)[less-than-or-equals, slant]H(x,y)[less-than-or-equals, slant]min(F(x),G(y)) for all x,y in [-[infinity],[infinity]]. 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.

Keywords: Bounds; Copulas; Distribution; functions; Kendall's; tau; Quartiles; Quasi-copulas (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (13)

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