On Similarity Correlation of Probability Distributions

Abstract

In recent years there has been much attention to the analysis and comparison of different measures of similarity and dissimilarity of probability distributions. In this work, we consider such measures as functions defined on the set of probability distributions and satisfying given properties. Further, we consider a correlation function defined on the set of probability distributions and satisfying simple properties fulfilled for most of the known correlation and association coefficients considered in statistics. We discuss general methods of constructing correlation functions from similarity and dissimilarity functions. Finally, we introduced several new similarity, dissimilarity, and correlation functions on the set of probability distributions.