A New Index for Measuring the Difference Between Two Probability Distributions

This technical note proposes a new index for measuring the difference between two probability distributions, named distribution discrepancy index (DDI). The proposed distribution discrepancy index is derived based on the concepts of informity, cross-informity, and informity divergence in the recently proposed informity theory. It is defined as the ratio between the informity divergence of two probability distributions and the sum of the two informities. The proposed distribution discrepancy index ranges between 0 and 1, which makes its interpretation intuitive, simple, and meaningful. A low DDI value (e.g. close to 0) indicates that the difference between the two probability distributions is small. A high DDI value (e.g. close to 1) indicates that the difference is large. Two examples are presented to demonstrate the application of the proposed distribution discrepancy index.