On Some Multivariate Extensions to Zenga Curve: Properties and Applications

2026-04-12

AI Summary

Traditional inequality measures struggle to capture the joint inequality structure of multidimensional socioeconomic variables. This study addresses this limitation by extending the Zenga inequality measure to the bivariate setting for the first time, constructing a Zenga surface and a vector-valued Zenga curve based on the bivariate quantile function, along with corresponding nonparametric estimation methods. The proposed framework enables a nuanced characterization of the distributional features of multidimensional inequality. Empirical analysis focusing on digital inequality reveals complex patterns of disparity between national broadband penetration rates and digital literacy levels across countries, thereby demonstrating the effectiveness and practical utility of the method.

Technology Category

Game Theory and Economic Paradigms: Fair DivisionMachine Learning: Calibration & Uncertainty QuantificationData Mining & Knowledge Management: Mining of Visual, Multimedia & Multimodal Data

Application Category

Web Mining and Content Analysis: Web measurementsEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystemsSecurity and Privacy: Large-scale security measurements

Abstract

Measures of inequality are often limited in their ability to capture multidimensional aspects that arise from the joint distribution of multiple socio-economic variables. In this paper, we develop bivariate extensions of the Zenga inequality measure using bivariate quantile functions. We propose new bivariate Zenga surfaces and study their theoretical properties. A vector-valued bivariate Zenga curve is also introduced to provide a more detailed characterization of inequality. A non-parametric estimator is proposed and methods are evaluated through simulation studies and applied to the analysis of digital inequality across countries using indicators such as broadband penetration and digital literacy. The results highlight the effectiveness of the proposed framework in capturing multidimensional inequality.

Problem

• multidimensional inequality
• Zenga curve
• bivariate quantile functions
• digital inequality
• socio-economic variables

Innovation

• bivariate Zenga curve
• multidimensional inequality
• bivariate quantile functions
• non-parametric estimation
• digital inequality