Distance Metrics for Gamma Distributions

Abstract

Here I present the analytic form of two common distance metrics, the symmetrised Kullback-Leibler Divergence and the Kolmogorov-Smirnov statistic, as well as an extension of the Kolmogorov-Smirnov statistic for comparing theoretical gamma distributions. In doing so, I also present the analytic solution to the intersection of two gamma distributions. Lastly, I provide examples that demonstrate the similarity between these distance metrics and their usefulness in describing the separability of gamma distributions.