Revisiting poverty measures using quantile functions
DOI:
https://doi.org/10.25071/1874-6322.40616Keywords:
Poverty measures, Sen index, quantile function, income modelsAbstract
In this article we redefine various poverty measures in literature in terms of quantile functions instead of distribution functions in the prevailing approach. This enables provision for alternative methodology for poverty measurement and analysis along with some new results that are difficult to obtain in the existing framework. Several flexible quantile function models that can enrich the existing ones are proposed and their utility is demonstrated for real data.
References
Aggarwal, V. (1984). On optimum aggregation of income distribution data. Sankhya: The Indian Journal of Statistics, Series B, 46:343–355.
Atkinson, A. B. (1987). On the measurement of poverty. Econometrica: Journal of the Econometric Society, 55:749–764.
Chakravarty, S. R. (1983). Ethically flexible measures of poverty. The Canadian Journal of Economics, 16:74–85.
Chakravarty, S. R. (2019). On Shorrocks’ reinvestigation of the Sen poverty index. Poverty, Social Exclusion and Stochastic Dominance, pages 27–29.
Chotikapanich, D. (1993). A comparison of alternative functional forms for the Lorenz curve. Economics Letters, 41:129–138.
Clark, S., Hemming, R., and Ulph, D. (1981). On indices for the measurement of poverty. The Economic Journal, 91:515–526.
Foster, J., Greer, J., and Thorbecke, E. (1984). A class of decomposable poverty measures. Econometrica: Journal of the Econometric Society, 52:761–766.
Gilchrist, W. (2000). Statistical Modelling with Quantile Functions. Chapman and Hall/CRC, London, UK.
Gupta, M. R. (1984). Functional form for estimating the Lorenz curve. Econometrica, 52:1313–1314.
Hagenaars, A. (1987). A class of poverty indices. International Economic Review, 28:583–607.
Hagenaars, A. J. (2017). The definition and measurement of poverty. In Economic Inequality and Poverty, pages 134–156. Routledge.
Haridas, H. N., Nair, N. U., and Nair, K. R. M. (2008). Modelling income using the generalised lambda distribution. Journal of Income Distribution, 17(2):37–51.
Hosking, J. R. (1994). The four-parameter kappa distribution. IBM Journal of Research and Development, 38:251–258.
Houghton, J. C. (1978). Birth of a parent: The wakeby distribution for modeling flood flows. Water Resources Research, 14:1105–1109.
Kakwani, N. (1980). On a class of poverty measures. Econometrica: Journal of the Econometric Society, 48:437–446.
Kakwani, N. C. and Podder, N. (1973). On the estimation of Lorenz curves from grouped observations. International Economic Review, 14:278–292.
Karian, Z. A. and Dudewicz, E. J. (2000). Fitting Statistical Distributions: The Generalized Lambda Distribution and Generalized Bootstrap Methods. Chapman and Hall/CRC.
Mudholkar, G. S. and Kollia, G. D. (1994). Generalized Weibull family: a structural analysis. Communications in Statistics-Theory and Methods, 23:1149–1171.
Nair, N. U., Nair, K. M., and Haridas, H. N. (2008). Some properties of income gap ratio and truncated gini coefficient. Calcutta Statistical Association Bulletin, 60:245–254.
Nair, N. U., Sankaran, P. G., and Balakrishnan, N. (2013). Quantile-Based Reliability Analysis. Springer, US.
Nair, N. U. and Vineshkumar, B. (2022). Cumulative entropy and income analysis. Stochastics and Quality Control, 37:165–179.
Ortega, P., Martin, G., Fernandez, A., Ladoux, M., and Garcia, A. (1991). A new functional form for estimating Lorenz curves. Review of Income and Wealth, 37:447–452.
Ramberg, J. S. and Schmeiser, B. W. (1972). An approximate method for generating symmetric random variables. Communications of the ACM, 15:987–990.
Rohde, N. (2009). An alternative functional form for estimating the Lorenz curve. Economics Letters, 41:21–29.
Sen, A. (1976). Poverty: an ordinal approach to measurement. Econometrica: Journal of the Econometric Society, 44:219–231.
Sen, P. K. (1986). The gini coefficient and poverty indices: some reconciliations. Journal of the American Statistical Association, 81:1050–1057.
Shorrocks, A. F. (1995). Revisiting the Sen poverty index. Econometrica: Journal of the Econometric Society, 63:1225–1230.
Takayama, N. (1979). Poverty, income inequality, and their measures: Professor Sen’s axiomatic approach reconsidered. Econometrica: Journal of the Econometric Society, 47:747–759.
Tarsitano, A. et al. (2004). Fitting the generalized lambda distribution to income data. In COMPSTAT’2004 Symposium, pages 1861–1867. Springer.
Tarsitano, A. et al. (2006). A new Q-Q plot and its application to income data. Statistica & Applicazioni, 4.
Thon, D. (1979). On measuring poverty. Review of Income and Wealth, 25:429–439.
Thon, D. (1983). A poverty measure. The Indian Economic Journal, 30:285–307.
Watts, H. W. (1969). An economic definition of poverty. In Moynitian, D Ed. On Understanding Poverty, pages 316–329.
Xu, K. (2020). The Sen-Shorrocks-Thon index of poverty intensity. In Encyclopedia of Quality of Life and Well-Being Research, pages 1–3. Springer.
Yang, L. (2017). The relationship between poverty and inequality: Concepts and measurements. Working paper, Centre for Analysis of Social Exclusion, London School of Economics.


