Middle Income Positioning and Population Measurement Based on The Lorenz Curves

Middle Income Positioning and Population Measurement Based on The Lorenz Curves

Jincan Liu Xin Liu

College of Civil Engineering and Architecture, Hainan University, Renmin Road No.58, Meilan District, Haikou, Hainan, China

School of Mathematics and Statistics, Xidian University Xifeng Road No.266, Changan District, Xian, Shaanxi, China

Corresponding Author Email: 
1850753011@qq.com, 970749805@qq.com
15 March 2017
15 April 2017
30 March 2017
| Citation



In this article, a new Lorenz curve model is proposed, and the model is fitted with the given data. Thus the estimates of the parameters and the value of mean squared error(MSE), maximal absolute error(MAS), and mean absolute error(MAE) are got, It can be concluded that the proposed model is better than the classical models. Then an income space method is improved to make up the defects of the classical ones. Finally, the new Lorenz curve model and the improved income space method are applied to analyze the data from Problem E in the National Graduate Mathematical Contest in Modeling in 2013, and some favorable results are got.


Lorenz curve, Middle income, Income distribution, Gini coefficient

1. Introduction
2. The New Proposed Lorenz Curve Model
3. The Improved Income Space Method
4. Results and Discussion
5. Conclusion

This work was supported by the Natural Science Foundation of Hainan Province under grant No.20167251.


1. V. Aggarwal, On the optimum aggregation of income distribution data, 1984, Sankhyā: The Indian Journal of Statistics, Series B, vol. 46, no. 3, pp. 343-355.

2. D. Chotikapanich, R. Valenzuela, D.S.P. Rao, Global and regional inequality in the distribution of income: estimation with limited and incomplete data, 1997, Empirical Economics, vol. 22, no. 4, pp. 533-546.

3. K.L. Gupta, Finance and Economic Growth in Developing Countries, 1984, London: Croom Helm, vol. 52, no. 3.

4. T. Ogwang, U.L.G. Rao, A new functional form for approximating the Lorenz curve, 1996, Economics Letters, vol. 52, no. 1, pp. 21-29.

5. H.C. Jing, Coverage holes recovery algorithm based on nodes balance distance of underwater wireless sensor network, 2014, International Journal on Smart Sensing and Intelligent Systems, vol. 7, no. 4, pp. 1890-1907.

6. H.C. Jing, Node deployment algorithm based on perception model of wireless sensor network, 2015, International Journal of Automation Technology, vol. 9, no. 3, pp. 210-215.

7. H.C. Jing, Routing optimization algorithm based on nodes density and energy consumption of wireless sensor network, 2015, Journal of Computational Information Systems, vol. 11, no. 14, pp. 5047-5054.

8. H.C. Jing, The Study on the Impact of Data Storage from Accounting Information Processing Procedure, 2015, International Journal of Database Theory and Application, vol. 8, no. 3, pp. 323-332.

9. Z. Wang, N.G. Yew-Kwang, R. Smith, A General Method for Creating Lorenz Curves, 2011, Review of Income and Wealth, vol. 133, no. 3, pp. 561-582.

10. Z. Wang, R. Smith, A Hybrid Method for Creating Lorenz Curves with An Application to Measuring World Income Inequality, 2013, Monash Economics Working Papers, vol. 255, no. 16, pp. 7517-7520.

11. P. Ortega, G. Martin, A. Fernandez, M. Ladoux, A. García, A new functional form for estimating Lorenz curves, 1991, Review of Income and Wealth, vol. 37, no. 4, pp. 447-452.

12. M.O. Haque, Income elasticity and economic development: Methods and applications, 2005, Advanced Studies in Theoretical & Applied Econometrics, vol. 42.

13. R.H. Rasche, Functional Forms for estimating the Lorenz curve: comment, 1980, Econometrica, vol. 48, no. 4, pp. 1061-1062.

14. J.E. Foster, M.C. Wolfson, Polarization and the decline of the middle class: Canada and the U.S, 2009, Journal of Economic Inequality, vol. 8, no. 2, pp. 247-273.

15. D. Chotikapanich, D.S.P. Rao, K.K. Tang, Estimating income Inequality in china using Grouped data and the generalized Beta distribution, 2007, Review of Income and Wealth, vol. 53, no. 1, pp. 127-147.

16. Problem E in the National Graduate Mathematical Contest in Modeling in 2013 (interlinkage: http://gmcm.seu.edu.cn/).