On Some Multivariate Extensions to Zenga Curve: Properties and Applications

TL;DR

This paper introduces multivariate extensions of the Zenga inequality measure using bivariate quantile functions, providing new tools for analyzing multidimensional inequality in socio-economic data.

Contribution

It develops bivariate Zenga surfaces, a vector-valued Zenga curve, and a non-parametric estimator, advancing the analysis of multidimensional inequality.

Findings

Proposed bivariate Zenga measures effectively capture digital inequality.

Simulation studies validate the estimator's performance.

Application to country data demonstrates practical utility.

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.