A New Index for Measuring the Non‐Uniformity of a Probability Distribution

This technical note proposes a new index to quantitatively measure the non‐uniformity of a probability distribution relative to a baseline uniform distribution, named as the “distribution non‐ uniformity index” (DNUI). The proposed DNUI is bounded between 0 and 1, where 0 indicates perfect uniformity and 1 indicates extreme non‐uniformity. It is appliable to both discrete and continuous cases. Several examples are provided to demonstrate the effectiveness of the proposed DNUI and compare it with two evenness measures.