Two New Indices for Measuring the Difference Between Two Probability Distributions

This paper proposes two new indices for measuring the difference between two probability distributions: one is named “distribution similarity index (DSI)” and the other is named “distribution discrepancy index (DDI)”. These two indices are derived based on the concepts of informity and cross-informity in the recently proposed informity theory. Both indices range between 0 and 1. A low DSI value or a high DDI value indicates a large difference between two probability distributions. A high DSI value or a low DDI value indicates a small difference. Three examples are provided to compare the proposed indices with existing similarity and discrepancy indices.