Abstract
The Gini index is a measure of the inequality of a distribution that can be derived from Lorenz curves. While commonly used in, e.g., economic research, it suffers from ambiguity via lack of Lorenz dominance preservation. Here, investigation of large sets of empirical distributions of incomes of the World’s countries over several years indicated firstly, that the Gini indices are centered on a value of 33.33% corresponding to the Gini index of the uniform distribution and secondly, that the Lorenz curves of these distributions are consistent with Lorenz curves of log-normal distributions. This can be employed to provide a Lorenz dominance preserving equivalent of the Gini index. Therefore, a modified measure based on log-normal approximation and standardization of Lorenz curves is proposed. The so-called UGini index provides a meaningful and intuitive standardization on the uniform distribution as this characterizes societies that provide equal chances. The novel UGini index preserves Lorenz dominance. Analysis of the probability density distributions of the UGini index of the World’s counties income data indicated multimodality in two independent data sets. Applying Bayesian statistics provided a data-based classification of the World’s countries’ income distributions. The UGini index can be re-transferred into the classical index to preserve comparability with previous research.
Highlights
Computational data science is a rapidly growing multidisciplinary field that uses advanced computing capabilities to understand and solve complex problem processes and systems [1]
The present analysis shows that a detailed investigation of the probability density function of the Gini indices resulted in the observation that a third or more of the Gini indices are distributed around a mean of 33.33% that corresponds to the Gini Index of a uniform distribution
Based on valid Lorenz curve approximation with a log-normal model of income distributions, the UGini index is highly correlated with the original raw Gini index while being Lorenz dominance preserving
Summary
Computational data science is a rapidly growing multidisciplinary field that uses advanced computing capabilities to understand and solve complex problem processes and systems [1]. It is aimed for extracting knowledge from data from various fields of research. The Gini index is used in economic data analyses such as the world’s countries’ income distributions [5, 6] and its consequences [7]. Comparative analysis of the world’s countries’ income inequalities is an active research topic [8,9,10,11,12].
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