標本合計が負の場合へ拡張されたジニ係数の評価

概要

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The Gini coefficient is one of the indices most typically used to evaluate inequality amongst samples. However, it is inappropriate for evaluating inequality when negative samples are included in the population. This is because a precondition of the coefficient is that all samples must be positive. In order to enable the coefficient to evaluate inequality in such cases, Chen et al. attempted to extend it. However, their extended coefficient cannot be used to evaluate inequality when the sum of the samples is less than 0. In this paper, we extended the geometric expression of the Gini coefficient in order to enable it to be used to evaluate inequality even if the sum of the samples is less than 0. In addition, we confirmed that the extended coefficient was exactly equal to the Gini coefficient when all of the samples in the population were positive. Furthermore, we considered the algebraic expression of the extended coefficient, and using this, we clarified that the extended coefficient satisfied both Pigou-Dalton's population principle and the extended transfer principle.