On the influence function for the Theil-like class of inequality measures

TL;DR

This paper unifies the influence functions of a broad class of inequality measures, including Gini and Atkinson, facilitating easier comparative analysis and advancing the understanding of their asymptotic properties.

Contribution

It provides a unified formula for the influence functions of all measures in the Theil-like family, enhancing analytical and comparative capabilities.

Findings

Unified influence function formula for Theil-like inequality measures

Simplified comparative analysis of inequality measures

Enhanced understanding of asymptotic behavior of these measures

Abstract

On one hand, a large class of inequality measures, which includes the generalized entropy, the Atkinson, the Gini, etc., for example, has been introduced in Mergane and Lo (2013). On the other hand, the influence function of statistics is an important tool in the asymptotics of a nonparametric statistic. This function has been and is being determined and analysed in various aspects for a large number of statistics. We proceed to a unifying study of the IF of all the members of the so-called Theil-like family and regroup those IF's in one formula. Comparative studies become easier.