Correlation Structure in Farlie-Gumbel-Morgenstern Distributions

Abstract

Several measures of dependence are examined for the Farlie-Gumbel-Morgenstern system, F, of joint distributions. Some bounds and relationships are shown for product-moment correlation coefficients and rank correlation coefficients. While the F system is an interesting construction for specified marginals, it is limited to describing weak dependence. A quality control application using a related screening variable is given.