This evaluation reveals new norm-based measures of inequality in income distributions, highlighting their analytical characterizations and practical significance.
Abstract Norm-based inequality measures are developed within the UD/RUD framework by applying L₁ and squared L₂ norms to the CDQF, QF, and their joint CDQF representations. All six indices satisfy scale, replication, and translation invariance, as well as anonymity, and their behavior under Pigou-Dalton transfers and subgroup decomposition is characterized analytically. CDQF-based indices combine the vertical and horizontal gaps, giving them representation decomposability and making L1,cq and L²2,cq the most informative overall measures of inequality. A Monte Carlo study on six contrasting income distributions corroborates these theoretical advantages, confirming finite, stable values even for mixed-sign and heavy-tailed supports. JEL Classification: C43 , D31 , D63
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Hamza et al. (2025) studied this question.