Abstract: The information contained in a discrete two-way contingency table can be decomposed into three independent components: row marginals, column marginals and cross-product ratios. The log-linear models and association models for ordered contingency tables demonstrate the richness and flexibility of considering these components separately. Holland and Wang (1987a) introduced the local dependence function, which mimics the cross-product ratios, for continuous bivariate densities. We proved that the local dependence function and two marginal densities uniquely determine the joint density. An iterative procedure to approximate the joint density was presented. Wang (1987) demonstrated this approach for the bivariate normal density. Different systems of bivariate distributions are examined to reveal their strength and limitation from a discrete perspective. Possible extensions are suggested.
Key words and phrases: Local dependence function, marginal-free, iterative margin-al replacement, systems of bivariate density functions.