Correlation structure in iterated Farlie-Gumbel-Morgenstern distributions

Abstract

SUMMARY In this note we determine the natural parameter space of the iterated Farlie-Gumbel-Morgenstern distribution, and thereby show that the maximum correlation is higher than was previously known. We also show that just one single iteration can result in tripling the covariance for certain marginals. Finally, we show that there exist no marginals for which the single iteration will bring about higher negative correlation.