Dependence function for continuous bivariate densities

Abstract

The notion of cross-product ratio for discrete two-way contingency table is extended to the case of continuous bivariate densities. This results in the “local dependence function” that measues the margin-free dependence between bivariate random variables. Properties and examples of the dependence function are discussed. The bivariate normal density plays a special role since it has constant dependence. Continuous bivariate densities can be constructed by specifying the dependence function along with two marginals in analogy to the construction of two-way contingency tables given marginals and patterns of interaction. The dependence function provides a partial ordering on bivariate dependence.