Exploring the Application of Quantile-Based Methods in Measuring Inequality and Distributional Differences
Posted: Oct 25, 2020
Abstract
The measurement of inequality and distributional differences represents a fundamental challenge across numerous disciplines, from economics and sociology to environmental science and public health. Traditional approaches to quantifying inequality have predominantly relied on summary statistics such as the Gini coefficient, Theil index, and various percentile ratios. While these measures provide valuable insights, they suffer from inherent limitations in capturing the full complexity of distributional patterns. This paper introduces a comprehensive framework for measuring inequality and distributional differences using quantile-based methods that leverage the complete distributional information. Our approach moves beyond the conventional paradigm of scalar inequality measures toward functional approaches that preserve the richness of distributional characteristics. We develop three novel quantile-based measures that address different aspects of distributional analysis: The Quantile Dispersion Index (QDI) measures dispersion across multiple quantiles simultaneously, the Distributional Asymmetry Metric (DAM) specifically targets asymmetric distributional changes, and the Quantile Overlap Coefficient (QOC) quantifies the degree of similarity between distributions.
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