基于ArcGis平台利用洛伦兹曲线对基尼系数的简化计算方法  

The simplified calculation method of Gini coefficient using Lorentz curve based on ArcGIS platform

作　　者：王立志[1,2] 宋红丽[1,2] 郁万妮 安娟[1,2] 吴希媛[1,2] 吴元芝[1,2] WANG Lizhi;SONG Hongli;YU Wanni;AN Juan;WU Xiyuan;WU Yuanzhi(Shandong Provincial Key Laboratory of Water and Soil Conservation and Environmental Protection,Linyi University,Linyi 276005,China;School of Resources and Environment,Linyi University,Linyi 276005,China)

机构地区：[1]临沂大学山东省水土保持与环境保育重点实验室,山东临沂276005 [2]临沂大学资源环境学院,山东临沂276005

出　　处：《高师理科学刊》2022年第5期71-75,89,共6页Journal of Science of Teachers＇College and University

基　　金：山东省本科教学改革研究项目(M2020296)。

摘　　要：基尼系数是以洛伦兹曲线为基础推导出来的.在实际应用中,一般用直接计算法、拟合曲线法、分组计算法和分解法等计算基尼系数.这几种方法可行,但缺点很明显,其计算方法有的比较粗糙,并且计算结果不够精确.基尼系数的值取决于洛伦兹曲线与绝对平均线之间面积的大小,可能有相同的基尼系数.为避免一般方法带来的误差,基于ArcGis平台,利用洛伦兹曲线对基尼系数简化计算.步骤为:(1)绘制洛伦兹曲线;(2)将洛伦兹曲线图标坐标进行统计,主要统计图标4个端点坐标,对角线坐标,以及洛伦兹曲线坐标,坐标值按照散点图的xy轴值进行定义,值为无量纲;(3)将xy轴坐标数据导入ArcGis平台里的ArcMap;(4)将导入文件转为shape格式线文件;(5)将shape格式线文件转为面文件;(6)计算面文件面积,计算基尼系数.该方法避免了复杂的积分过程,同时也避免了洛伦兹曲线解析式的描述,可以将误差降低到最小,同时简化的计算步骤,在计算效率方面具有较大的提高.Gini coefficient is derived from Lorentz curve.In practical application,direct calculation method is generally used.The Gini coefficient is calculated by fitting curve,grouping and factorization method.These methods are feasible,but the disadvantages are obvious.Some of the methods are rough and the results are not accurate.The Gini coefficient is determined by the area between Lorentz curve and absolute average line,and it may have the same Gini coefficient.In order to avoid the error caused by the general method,based on ArcGIS platform and the simplified calculation of Gini coefficient by using Lorentz curve.The steps are as follows:(1)Draw Lorentz curve.(2)The coordinates of Lorentz curve icons are counted,mainly including four end point coordinates,diagonal coordinates,and Lorentz curve coordinates.The coordinate values are defined according to the xy axis value of the scatter graph,and the value is dimensionless.(3)The xy coordinate data is imported into ArcMap in ArcGIS platform.(4)Converts the import file to shape format file,line file.(5)Converts the shape format line file to a polygon file.(6)Calculate the area of the file on the surface and calculate the Gini coefficient.This method avoids the complicated integration process,and avoids the description of Lorentz curve analytic formula.It can reduce the error to the minimum,and simplify the calculation steps,and improve the calculation efficiency greatly.

关 键 词：基尼系数 洛伦兹曲线 ARCGIS平台 计算方法 计量地理学 

分 类 号：K90[历史地理—人文地理学]