## The Annals of Statistics

### Bivariate Distributions with Given Marginals

Ward Whitt

#### 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

https://projecteuclid.org/euclid.aos/1176343660

Digital Object Identifier
doi:10.1214/aos/1176343660

Mathematical Reviews number (MathSciNet)
MR426099

Zentralblatt MATH identifier
0367.62022

JSTOR