Copula-Based Mutual Information Measures and Mutual Entropy: A Brief Survey

The notion of divergence is often used to measure the separation between two parametric densities with possible applications on differential geometry to problems of parametric inference among others. Among them, in this paper, we discuss several popular divergence (alias pseudo-distance) measures such as the power divergence, Kullback–Leibler information, J-divergence, Hellinger distance, Bhattacharya divergence, \(\alpha\) -divergence, and so on. A wide range of discussion in terms of properties, relationship among these measures, and results related to distance between two probability distributions are derived via copula functions. In addition, several dependency concepts such as weak negative dependence etc. are visited in terms of copula based divergence measures and important inequalities are obtained.