基于三次Hermite插值与线性规划的Lorenz曲线逼近方法

Lorenz Curve Approximation Based on Cubic Hermite Interpolation and Linear Programming

Lorenz曲线和Gini系数是收入分配分析的重要工具。文章通过对《中国统计年鉴》2014年发布的城镇和农村分别的收入分配数据进行加总得到全国的Lorenz曲线及Gini系数。具体做法是在已知城镇和农村Lorenz曲线分组数据的基础上,运用线性规划的方法求得的各分割点处的导数值。目的是使得分段Hermite插值后的整体曲线保持为单调上升的光滑凸曲线。利用这种方法首先得到城镇和农村各自的Lorenz曲线,然后再对城镇和农村的Lorenz曲线进行加总得到全国的Lorenz曲线及全国的Gini系数。

Lorenz curve and Gini index are important tools to measure the income distribution of the residents. This paper gets national Lorenz curves and Gini indexes of whole China by aggregating the Lorenz curves of urban and rural area according to the data reported by China Statistics Yearbook published in 2014. In order to obtain integral curve of piecewise Hermite interpolation as a smooth convex curve, based on the grouped data of the known Lorenz curves of urban and rural areas, we use the linear programming method to obtain the derivative values at the each partition point of Hermite interpolation. Using this method, we first get the Lorenz curve of the urban and rural areas respectively, and then get the Lorenz curve of the whole country and the Gini index of the country by aggregate the Lorenz curve of urban and rural areas.