The HUA Index:A Robust, Bounded Measure of Dispersion for Positive Data Streams

The coefficient of variation (CV) is a popular scale-free dispersion metric, but it is notoriously sensitive to extreme observations. This paper proposes the HUA Index—a simple, bounded (0 to 1), and robust alternative—defined as the ratio of the inter-quartile range (IQR) to the sum of the sample median and the median absolute deviation (MAD). Mathematical proofs establish its scale-invariance and strict upper bound. Monte-Carlo simulations under log-normal, Student-t, and Pareto distributions show that the HUA Index incurs less than 5% bias when 10% of the sample values are gross outliers, whereas CV inflates by more than 500%. Two case studies (urban PM2.5 concentrations and S&P 500 log-returns) highlight the index’s stability in real-world heavy-tailed data.