Statistical Dependence: Copula Functions and Mutual Information Based Measures

Accurately and adequately modelling and analyzing relationships in real random phenomena involving several variables are prominent areas in statistical data analysis. Applications of such models are crucial and lead to severe economic and financial implications in human society. Since the beginning of developments in Statistical methodology as the formal scientific discipline, correlation based regression methods have played a central role in understanding and analyzing multivariate relationships primarily in the context of the normal distribution world and under the assumption of linear association. In this paper, we aim to focus on presenting notion of dependence of random variables in statistical sense and mathematical requirements of dependence measures. We consider copula functions and mutual information which are employed to characterize dependence. Some results on copulas and mutual information as measure of dependence are presented and illustrated using real examples. We conclude by discussing some possible research questions and by listing the important contributions in this area.