基于对数正态分布的洛伦兹曲线与基尼系数

Lorenz Curve and GINI Coefficient under Condition of Lognormal Distribution

在对数正态分布这一特定条件下,本文对洛伦兹曲线与基尼系数进行了研究,结果表明,在这一条件下,社会经济指标ζ的洛伦兹曲线具有对称性,与基尼系数一一对应,他们完全取决于该指标取对数后的均方差σ=Dlnζ,只要测算出σ,根据本文提出的方程就可以绘制出洛伦兹曲线、计算出基尼系数。实证分析表明,社会经济规模指标服从对数正态分布。因此,本文的结果在较广的范围具有指导意义和实用价值。最后,举例说明本文方法的应用及其正确性。

This paper deals with the problem of Lorenz curve and GINI index. It concludes that under condition of logarithm normal distribution, Lorenz curves of social or economical indicators ζ has characteristic of symmetry and corresponds to GINI coefficients one by one, which all depend on σ=Dlnζ. As long as σ is given by calculating, according to the formulas given in the paper, the corresponding Lorenz curve and GINI index can be drawn and calculated. Based on empirical analysis, it is shown that social or economic indicators reflecting system scale obey the lognormal distribution so that the results of this paper have practical values. Finally, some examples are used to illustrate the results of new method about calculating GINI index and to show the validity of our results.