DOI: 10.3390/risks14110248 ISSN: 2227-9091

Inequality Measurement for Real-Valued Random Variables via Absolute Moments

Xuehua Yin, Dan Zhu
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This paper proposes a novel statistical index based on absolute moments. This new index generalizes the classical Gini coefficient, extending the index’s applicability to real-valued random variables, including those that may take negative values. We investigate the fundamental properties of the index, derive several equivalent representations, and examine the sample estimator of the G-index, establishing its strong consistency and asymptotic normality. Furthermore, we explore the relationship between the proposed index and two entropy measures, and present both theoretical and numerical examples.

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