**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31103

##### Measurement of the Bipolarization Events

**Authors:**
Stefan V. Stefanescu

**Abstract:**

**Keywords:**
Income Distribution,
gini coefficient,
Bipolarization phenomenon,
poverty measure

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1076076

**References:**

[1] A. Agresti, An introduction to categorical data analysis. New York: Wiley Series in Probability and Statistics, 1996.

[2] C. D'Ambrosio, "Household characteristics and the distribution of income in Italy - An application of social distance measures," The Review of Income and Wealth, vol. 47, no. 1, pp. 43-64, 2001.

[3] A. B. Atkinson, "On the measurement of inequality." Journal of Economic Theory, no. 2, pp. 244-263, 1970.

[4] D. J. Bartolomew, The statistical approach to social measurement. London: Academic Press, 1996.

[5] N. Bhattacharya, and B. Mahalanobis, "Regional disparities in household consumption in India," Journal of the American Statistical Association, vol. 62, pp. 143-161, 1967.

[6] F. Bourguignon, "Decomposable income inequality measures," Econometrica, vol. 47, pp. 901-920, 1979.

[7] A. Chateauneuf, T. Gajdos, and P. H. Wilthien, "The principle of strong diminishing transfer," Journal of Economic Theory, vol. 103, pp. 311- 333, 2002.

[8] F. A. Cowell, "On the structure of additive inequality measures," Review of Economic Studies, vol. 47, pp. 521-531, 1980.

[9] F. A. Cowell, and S. P. Jenkins. "How much inequality can we explain ? A methodology and an application to the United States," The Economic Journal, vol. 105, pp. 421-430, 1995.

[10] J. B. Davies, and A. Shorrocks, "Optimal grouping of income and wealth data," Journal of Econometrics, vol. 42, pp. 97-108, 1989.

[11] J. Esteban, and D. Ray, "On the measurement of polarization," Econometrica, vol. 62 , no. 4, pp. 819-852, 1994.

[12] J. Esteban, and D. Ray, "Conflict and distribution," Journal of Economic Theory, vol. 87, pp. 379-415, 1999.

[13] J. Esteban, C. Gradin, and D. Ray, "Extension of a measure of polarization with application to the income distribution of five OECD countries," Maxwell School of Citizenship and Public Affairs, Syracuse University, New York, Working paper no. 218, November 1999.

[14] B. S. Everitt, S. Landau, and M. Leese, Cluster analysis. London: Arnold, 2001.

[15] J. Foster, and A. K. Sen, On economic inequality. Oxford: Clarendon Press, 1997.

[16] J. E. Foster, and A. A. Shneyerov, "Path independent inequality measures," Journal of Economic Theory, Oxford, vol. 91, no. 2, pp. 199- 222, 2000.

[17] M. Fournier, "Inequality decomposition by factor component - A new approach illustrated on the Taiwanese case," CERDI, Université d-Auvergne, November 1999.

[18] J. Gastwirth, "The estimation of a family of measures of economic inequality," Journal of Econometrics, no. 3, pp. 61-70, 1975.

[19] C. Gradin, "Polarization by sub-populations in Spain, 1973-1991," Review of Income and Wealth, vol. 46, no. 4, pp. 457-474, December 2000.

[20] P. E. Hart, "The comparative statistics and dynamics of income distributions," Journal of the Royal Statistical Society, vol. 139, pp. 108- 125, 1976.

[21] N. C. Kakwani, "Statistical inference in the measurement of poverty," Review of Economics and Statistics, vol. 75, no. 3, pp. 632-639, 1993.

[22] C. Kleiber, and S. Kotz, Statistical size distributions in economics and actuarial sciences. New Jersey: John Wiley & Sons - Interscience, 2003.

[23] J. O. Lanjouw, and P. Lanjouw, "How to compare apples and oranges - Poverty measurement based on different definitions of consumption," Review of Income and Wealth, vol. 47, no. 1, pp. 25-42, 2001.

[24] A. W. Pedersen, "Inequality as relative deprivation - Theoretical issues and implications for empirical research," preprint ISA RC19 Conference 2001, "Old a new social inequalities", University of Oviedo, September 2001.

[25] G. Pyatt, "On the interpretation and disaggregation of Gini coefficient," The Economic Journal, vol. 86, pp. 243-255, 1976.

[26] F. Schmid, "A general class of poverty measures," Statistical Papers, vol. 34, pp. 189-211, 1993.

[27] A. K. Sen, On economic inequality. Oxford: Oxford University Press, 1973.

[28] A. F. Shorrocks, "The class additively decomposable inequality measures," Econometrica, vol. 48, pp. 613-625, 1980.

[29] A. F. Shorrocks, "Inequality decomposition by population subgroups," Econometrica, vol. 52, pp. 1369-1385, 1984.

[30] P. Stefanescu, and S. Stefanescu, "Extending the Gini index to measure inequality and poverty," Economic Computation and Economic Cybernetics Studies and Research, vol. 35, no. 1-4, pp. 145- 154, 2001.

[31] P. Stefanescu, and S. Stefanescu, "Comparing Gini index with three other concentration measures," Economic Computation and Economic Cybernetics Studies and Research, vol. 36, no. 1-4, pp. 173-184, 2002.

[32] P. Stefanescu, and S. Stefanescu, "The polarization index for bounded exponential distributions," Economic Computation and Economic Cybernetics Studies and Research, vol. 40, no. 3-4, pp. 211-218, 2006.

[33] P. Stefanescu, and S. Stefanescu, "The properties of a polarization index for bounded exponential distributions," U. P. B. - Scientific Bulletin, Series A : Applied Mathematics and Physics, vol. 68, no. 4, pp. 9-20, 2006.

[34] P. Stefanescu, and S. Stefanescu, "The Monte Carlo estimation of a polarization index for an arbitrary distribution," Economic Computation and Economic Cybernetics Studies and Research, vol. 41, no. 3-4, pp. 181-192, 2007.

[35] S. Stefanescu, "Measuring the socio-economic bipolarization phenomenon," Romanian Journal of Economic Forecasting, vol. 9, no. 1, pp. 149-161, 2008.

[36] K. Y. Tsui, "Multidimensional inequality and multidimensional entropy measures - An axiomatic derivation," Social Choice and Welfare, vol. 16, no 1, pp. 145-157, 1999.

[37] B. Wilfling, "Lorenz ordering of power function order statistics," Statistics & Probability Letters, vol. 30, pp. 313-319, 1996.

[38] M. Wolfson, "When inequalities diverge," American Economic Review, vol. 84, no. 2, pp. 353-358, 1994.

[39] M. Wolfon, "Divergent inequalities - Theory and empirical results," The Review of Income and Wealth, vol. 43, no. 4, pp. 401-422, 1997.

[40] S. Yitzhaki, "Economic distance and overlapping of distributions," Journal of Econometrics, vol. 61, pp. 147-159, 1994.

[41] X. Zhang, and R. Kanbur, "What difference do polarization measures make ? - An application to China," Journal of Development Studies, vol. 37, pp. 85-98, 2001.

[42] C. Zoli, "Intersecting generalized Lorenz curves and the Gini index," Social Choice and Welfare, vol. 16, pp. 183-196, 1999.