Some features of a new measure of income inequality based on the ratios between lower and upper medians

Mirzaei, Shahryar; Makhdoom, Iman

doi:10.22075/ijnaa.2026.36731.5390

Some features of a new measure of income inequality based on the ratios between lower and upper medians

Articles in Press

Document Type : Research Paper

Authors

Shahryar Mirzaei ¹

Iman Makhdoom ²

¹ Department of statistics, Payame Noor University, Tehran, Iran.

² Department of Statistics, Payame Noor University, Tehran, Iran

10.22075/ijnaa.2026.36731.5390

Abstract

This paper introduces a median‑based measure of income inequality, defined as the ratio between the lower and upper medians of the income distribution. The index is defined pointwise, and its corresponding inequality curve is presented. We examine the essential properties of the index, including normalization, scale invariance, location sensitivity, and the Pigou–Dalton transfer principle. The behavior of the inequality curve is investigated within common parametric income models. A suitable estimator is proposed, and its strong consistency and asymptotic normality are established. Additionally, a stochastic order based on the proposed curve is defined and studied. Simulation studies show that the proposed estimator performs competitively compared to the Gini coefficient in terms of bias, mean squared error, and coverage probabilities. Finally, the measure is applied to real-household income data, illustrating its practical usefulness.

Keywords

Income inequality curve

Lower and upper medians

Gini coefficient

Quantile functions

Median inequality index

Subjects