Bivariate Distributions with Given Marginals
Bivariate Distributions with Given Marginals
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 …