Exploratory Data Analysis with Bivariate Dependence Functions

Dependence functions are used to construct joint distributions with fixed marginals. They can shed light on relationships among associated random variables. Many dependence functions have been proposed and standardized. However, there has not been an attempt to understand why certain dependence functions are used and what makes certain dependence functions better than others in solving practical problems. In this paper, we compare an approach to dependence function which identifed and characterized the density weighting function and a class of bivariate densities constructed from polygonal covariance characteristic that would be flexible enough to capture various dependence structures. And, we also use the copulas for dependent random variables to compare the effects behind the dependence function.