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Norm-based measures of inequality: A property-focused evaluation
Muhammad Hamza1, Beomsu Baek2, Joongyang Park2
1Department of Bio and Medical Big Data, Gyeongsang National University, Jinju-si, Gyeongsangnam-do, Republic of Korea.
Plos One
|April 21, 2026
Summary
New norm-based inequality measures are introduced using the cumulative distribution and quantile function (CDQF) framework. These advanced measures offer superior informativeness and stability across various income distributions.
Area of Science:
- Economics
- Econometrics
- Statistics
Background:
- Inequality measurement is crucial for socioeconomic analysis.
- Existing measures may lack informativeness or stability in certain distributions.
- The unequally distributed/relative unequally distributed (UD/RUD) framework provides a basis for developing new indices.
Purpose of the Study:
- To develop novel norm-based inequality measures within the UD/RUD framework.
- To evaluate the theoretical properties and practical performance of these new indices.
- To enhance the informativeness and robustness of inequality measurement.
Main Methods:
- Application of L1 and squared L2 norms to the cumulative distribution and quantile function (CDQF) and quantile function (QF).
- Analytical examination of properties like scale invariance, anonymity, and Pigou-Dalton transfers.
- Monte Carlo simulations on diverse income distributions.
Main Results:
- Six new inequality indices were developed, maintaining key invariance properties.
- Indices combining CDQF offer superior informativeness due to integrating vertical and horizontal gaps.
- Monte Carlo studies confirmed the theoretical advantages, showing stable values for various distributions.
Conclusions:
- The developed norm-based inequality measures, particularly those using CDQF, represent a significant advancement.
- These indices provide a more comprehensive and stable assessment of inequality.
- The findings support their utility in analyzing complex income distributions.
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