A nice estimation of Gini index and power Pen's parade
Under the assumption that an economic variable y such as income, is a power function of its rank among n individuals, we provide the coefficient of variation and the Gini index as functions of the power degree of the Pen's parade. In fact, knowing the power degree of the Pen's parade function, we obtain the coefficient of variation and a sharp analytical simple way to compute Gini index in terms of the power degree. Reciprocally, knowing, the coefficient of variation of a said variable, we can also provide the power degree of the corresponding Pen's parade, hence deducting its shape. Several examples are given to illustrate our methods. Special attention is given to countries' Gini indices of the World development indicators report 2009 (WDI 2009).
References listed on IDEAS
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- Shalit, Haim & Yitzhaki, Shlomo, 1984. " Mean-Gini, Portfolio Theory, and the Pricing of Risky Assets," Journal of Finance, American Finance Association, vol. 39(5), pages 1449-68, December.
- Stéphane Mussard & J. Sadefo Kamdem & Françoise Seyte & Michel Terraza, 2011.
"Quadratic Pen'S Parade And The Computation Of The Gini Index,"
Review of Income and Wealth,
International Association for Research in Income and Wealth, vol. 57(3), pages 583-587, 09.
- Stéphane Mussard & Jules Sadefo Kamdem & Françoise Seyte & Michel Terraza, 2010. "Quadratic Pen's Parade and the Computation of the Gini index," Cahiers de recherche 10-18, Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke.
- Tomson Ogwang, 2011. "QUADRATIC PEN's PARADES: SOME NEW RESULTS AND AN APPLICATION," Working Papers 1101, Brock University, Department of Economics, revised Dec 2011.
- Yitzhaki, Shlomo, 1982. "Stochastic Dominance, Mean Variance, and Gini's Mean Difference," American Economic Review, American Economic Association, vol. 72(1), pages 178-85, March.
- Milanovic, Branko, 1997. "A simple way to calculate the Gini coefficient, and some implications," Economics Letters, Elsevier, vol. 56(1), pages 45-49, September.
- Gastwirth, Joseph L, 1972. "The Estimation of the Lorenz Curve and Gini Index," The Review of Economics and Statistics, MIT Press, vol. 54(3), pages 306-16, August.
- Lerman, Robert I. & Yitzhaki, Shlomo, 1984. "A note on the calculation and interpretation of the Gini index," Economics Letters, Elsevier, vol. 15(3-4), pages 363-368.
- World Bank, 2009. "World Development Indicators 2009," World Bank Publications, The World Bank, number 4367.
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