The Annals of Statistics

Bivariate Distributions with Given Marginals

Ward Whitt

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Abstract

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.

Article information

Source
Ann. Statist. Volume 4, Number 6 (1976), 1280-1289.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176343660

Digital Object Identifier
doi:10.1214/aos/1176343660

Mathematical Reviews number (MathSciNet)
MR426099

Zentralblatt MATH identifier
0367.62022

JSTOR
links.jstor.org

Subjects
Primary: 62E10: Characterization and structure theory
Secondary: 62E25 62H05: Characterization and structure theory 62H20: Measures of association (correlation, canonical correlation, etc.)

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

Citation

Whitt, Ward. Bivariate Distributions with Given Marginals. Ann. Statist. 4 (1976), no. 6, 1280--1289. doi:10.1214/aos/1176343660. http://projecteuclid.org/euclid.aos/1176343660.


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