《计算机应用研究》|Application Research of Computers

基于三角函数的洛伦兹曲线模型构造研究

Constructions of Lorenz curves based on trigonometric functions

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作者 丁恒,李延来,熊升华,陈振颂
机构 西南交通大学 a.交通运输与物流学院;b.综合交通运输智能化国家地方联合工程实验室,成都 610031
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文章编号 1001-3695(2014)11-3273-08
DOI 10.3969/j.issn.1001-3695.2014.11.018
摘要 为构造具有高拟合精度的洛伦兹曲线模型,提出两类基于三角函数的单参数洛伦兹曲线模型,进而通过对两类基本洛伦兹曲线的复合、加权积以及凸组合等方式构造一系列拓展洛伦兹曲线。实例研究表明,Pareto族曲线与三角函数型曲线的组合曲线对实际数据的拟合精度高于单独使用三角函数型曲线或单独使用Pareto族曲线,验证了基于三角函数的洛伦兹曲线模型构造是对既有洛伦兹曲线类型的有效拓展。
关键词 洛伦兹曲线模型;组合曲线;三角函数;洛伦兹序
基金项目 国家自然科学基金资助项目(71371156,70971017,71401142)
西南交通大学优秀博士学位论文培育资助项目
本文URL http://www.arocmag.com/article/01-2014-11-018.html
英文标题 Constructions of Lorenz curves based on trigonometric functions
作者英文名 DING Heng, LI Yan-lai, XIONG Sheng-hua, CHEN Zhen-song
机构英文名 a. School of Transportation & Logistics, b. Nation & Region Combined Engineering Laboratory of Intelligentizing Integrated Transportation, Southwest Jiaotong University, Chengdu 610031, China
英文摘要 To construct Lorenz curves of high fitting precision, this paper put forward two single-parameter models for Lorenz curves.Furthermore, it constructed a set of extended Lorenz curves by means of ways of such as compound, the weighted product and the convex combination, etc. based on the two proposed models. An illustration example shows that, compared with utilizing the Lorenz curves of trigonometric forms or the Lorenz curves of Pareto distribution separately, the Lorenz curves generated by the combination the Lorenz curves of trigonometric forms and the Lorenz curves of Pareto distribution have higher fitting precision, which verify the Lorenz curves of trigonometric forms are effective extensions of the existing ones.
英文关键词 Lorenz curves; combined curves; trigonometric functions; Lorenz ordering
参考文献 查看稿件参考文献
  [1] ATKINSON A B. On the measurement of inequality[J] . Journal of Economic Theory, 1970, 2(3):244-263.
[2] KAKWANI N C. Applications of Lorenz curves in economic analysis[J] . Econometrica, 1977, 45(3):719-727.
[3] KAKWANI N. Welfare ranking of income distributions[J] . Advances in Econometrics, 1984, 3:191-213.
[4] 厉以宁, 秦宛顺. 现代西方经济学概论[M] . 2版. 北京:北京大学出版社, 1992.
[5] SARABIA J M, CASTILLO E, SLOTTJE D J. An ordered family of Lorenz curves[J] . Journal of Econometrics, 1999, 91(1):43- 60.
[6] SCHADER M, SCHMID F. Fitting parametric Lorenz curves to grouped income distributions:a critical note[J] . Empirical Economi-cs, 1994, 19(3):361-370.
[7] KAKWANI N C, PODDER N. Efficient estimation of the Lorenz curve and associated inequality measures from grouped observations[J] . Econometrica, 1976, 44(1):137-148.
[8] RASCHE R H, GAFFNEY J, KOO A Y C. et al. Functional forms for estimating the Lorenz curve[J] . Econometrica, 1980, 48(4):1061-1062.
[9] GUPTA M R. Functional forms for estimating the Lorenz curve[J] . Econometrica, 1984, 52(5):1313-1314.
[10] BASMANN R L, HAYES K J, SLOTTJE D J, et al. A general functional form for approximating the Lorenz curve[J] . Journal of Econo-metrics, 1990, 43(1):77-90.
[11] ORTEGA P, MARTIN G, FERNANDEZ A, et al. A new functional form for estimating Lorenz curves[J] . Review of Income and Wealth, 1991, 37(4):447- 452.
[12] CHOTIKAPANICH D. A comparison of alternative functional forms for the Lorenz curve[J] . Economics Letters, 1993, 41(2):129-138.
[13] OGWANG T, GOURANGA RAO U L. A new functional form for approximating the Lorenz curve[J] . Economics Letters, 1996, 52(1):21-29.
[14] RYN H K, SLOTTJE D J. Two flexible functional form approaches for approximating the Lorenz curve[J] . Journal of Econometrics, 1996, 72(1):251-274.
[15] SARABIA J M. A hierarchy of Lorenz curves based on the generalized Tukey’s lambda distribution[J] . Econometric Reviews, 1997, 16(3):305-320.
[16] SARABIA J M, CASTILLO E, SLOTTJE D J. An exponential family of Lorenz curves[J] . Southern Economic Journal, 2001, 67(3):748-756.
[17] SARABIA J M, PASCUAL M. A class of Lorenz curves based on linear exponential loss functions[J] . Communications in Statistics-Theory and Methods, 2002, 31(6):925-942.
[18] ROHDE N. An alternative functional form for estimating the Lorenz curve[J] . Economics Letters, 2009, 105(1):61- 63.
[19] HELENE O. Fitting Lorenz curves[J] . Economics Letters, 2010, 108(2):153-155.
[20] 张奎, 王原君. Sarabia洛伦兹曲线模型的推广[J] . 应用数学, 2010, 23(3):501-507
[21] WANG Zu-xiang, NG Y K, SMYTH R. A general method for creating Lorenz curves[J] . Review of Income and Wealth, 2011, 57(3):561-582.
[22] OGWANG T, RAO U L G. Hybrid models of the Lorenz curve[J] . Economics Letters, 2000, 69(1):39- 44.
[23] SORDO M A, NAVARRO J, SARABIA J M. Distorted Lorenz curves:models and comparisons[J] . Social Choice and Welfare, 2013, 42(4):761-780.
[24] GASTWIRTH J L. A general definition of the Lorenz curve[J] . Econometrica, 1971, 39(6):1037-1039.
[25] PAKES A G. On income distributions and their Lorenz curves[R] . Nedlands, WA:Department of Mathematics, University of Western Australia, 1981.
[26] SARABIA J M, PRIETO F, SARABIA M. Revisiting a functional form for the Lorenz curve[J] . Economics Letters, 2010, 107(2):249-252.
[27] AGGARWAL V, SINGH R. On optimum stratification with proportional allocation for a class of Pareto distributions[J] . Communications in Statistics-Theory and Methods, 1984, 13(24):3107-3116.
[28] SHORROCKS A F. Ranking income distributions[J] . Economica, 1983, 50(197):3-17.
收稿日期 2013/11/28
修回日期 2014/1/2
页码 3273-3280
中图分类号 TP301.6
文献标志码 A