Contribuição ao estudo da medida de desigualdades - análise conjunta dos índices de Gini e Theil

Paulo R Nunes

DOI: 10.14209/sbrt.2019.1570553038

Evento: XXXVII Simpósio Brasileiro de Telecomunicações e Processamento de Sinais (SBrT2019)

Keywords:

Abstract

In this paper, the Gini, , and the Theil, , indices, which are used to measure inequality in a population, are jointly analyzed. The Theil index is a measure based on Information Theory, and can vary from 0 to ∞ if there is no limit on the size of the population. The Gini index is limited to the interval [0,1]. In a simple way, it is shown that the Theil index is the negative of a differential entropy, and, in the light of Information Theory, it is defined a new index, here called the equivalent slave population index, , that is a function of the Theil index and varies in the interval . Ideal wealth distribution functions and the well-known Pareto distribution are analyzed in the S-G plane. Results suggest superiority of the S index.

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