基于线性规划和带重节点三次样条的Lorenz曲线逼近方法
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摘要
Lorenz曲线和基尼系数对分析居民收入分布状况及财富分配不平等程度有重要作用。文章提出了一种基于线性规划和带重节点三次样条的Lorenz曲线逼近方法,并将此方法应用于2006—2012年中国城镇和农村居民收入的分组数据,得到了对应年度的城镇和农村的Lorenz曲线和基尼系数逼近。并利用加总方法,估计了2006—2012年度中国居民收入的加总Lorenz曲线及其对应的基尼系数。
Lorenz curve and Gini coefficient play an important role in analyzing the residents' income distribution and wealth distribution inequality. This paper proposes a Lorenz curve approximation method based on linear programming and cubic splines with multiple nodes, and applies this method to grouped data of China's urban and rural residents' income from 2006 to 2012 to obtain the corresponding annual Lorenz curve and Gini coefficient approximation of urban and rural areas. The paper also uses the summation method to estimate the aggregated Lorenz curve and its corresponding Gini coefficient of Chinese household income from 2006 to 2012.
Lorenz curve and Gini coefficient play an important role in analyzing the residents' income distribution and wealth distribution inequality. This paper proposes a Lorenz curve approximation method based on linear programming and cubic splines with multiple nodes, and applies this method to grouped data of China's urban and rural residents' income from 2006 to 2012 to obtain the corresponding annual Lorenz curve and Gini coefficient approximation of urban and rural areas. The paper also uses the summation method to estimate the aggregated Lorenz curve and its corresponding Gini coefficient of Chinese household income from 2006 to 2012.
引文
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[2]颜节礼,王祖祥.洛伦兹曲线模型研究综述和最新进展[J].统计与决策,2014,(1).
[3]Gastwirsh J L,Glauberman M.The Interpolation of the Lorenz Curve and Gini Index From Grouped Data[J].Econometrica,1976,44(3).
[4]Zhang W X,Wu Z M.Some Shape Preserving Quasi-interpolants to Non-uniformly Distributed Data by MQ-B-splines,Applied Mathematics[J].Journal of Chinese Universitys,2004,(2).
[5]梁英,贾丹丹,李强,梁学章.基于三次Hermite插值与线性规划的Lorenz曲线逼近方法[J].统计与决策,2017,(8).
[6]周蕴时,梁学章,常玉堂,马富明.数值分析[M].北京:高等教育出版社,2008.
[7]席少霖,赵凤治.最优化计算方法[M].上海:上海科学技术出版社,1983.
[8]林平,郭继强,费舒澜.中国城乡综合基尼系数测算的一种新改进[J].数量经济技术经济研究,2013,(11).
[9]Chen J D,Fang F Q,Hou W X,et al.Chinese Gini Coefficient From2005 to 2012,Based on20 Grouped Income Data Sets of Urban and Rural Residents[J].Journal of Applied Mathematics,2015.