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November, 1976 Bivariate Distributions with Given Marginals
Ward Whitt
Ann. Statist. 4(6): 1280-1289 (November, 1976). DOI: 10.1214/aos/1176343660


Bivariate distributions with minimum and maximum correlations for given marginal distributions are characterized. Such extremal distributions were first introduced by Hoeffding (1940) and Frechet (1951). Several proofs are outlined including ones based on rearrangement theorems. The effect of convolution on correlation is also studied. Convolution makes arbitrary correlations less extreme while convolution of identical measures on $R^2$ makes extreme correlations more extreme. Extreme correlations have applications in data analysis and variance reduction in Monte Carlo studies, especially in the technique of antithetic variates.


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Ward Whitt. "Bivariate Distributions with Given Marginals." Ann. Statist. 4 (6) 1280 - 1289, November, 1976.


Published: November, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0367.62022
MathSciNet: MR426099
Digital Object Identifier: 10.1214/aos/1176343660

Primary: 62E10
Secondary: 62E25 , 62H05 , 62H20

Keywords: Antithetic variates , Bivariate distributions , bivariate distributions with given marginals , extreme correlation , generating random variables , Monte Carlo , nearest random variables , rearrangement theorems , variance reduction

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 6 • November, 1976
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