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Sampling Distributions of Lorenz Curve and Gini Index of the Pareto Distribution
T. S. K. Moothathu
Sankhyā: The Indian Journal of Statistics, Series B (1960-2002)
Vol. 47, No. 2 (Aug., 1985), pp. 247-258
Published by: Indian Statistical Institute
Stable URL: http://www.jstor.org/stable/25052395
Page Count: 12
You can always find the topics here!Topics: Gini index, Lorenz curve, Maximum likelihood estimation, Mathematical moments, Income inequality, Econometrics, Sampling distributions, Maximum likelihood estimators, Random variables, Concentration ratio
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This paper presents the maximum likelihood estimators (MLEs) of Lorenz curve and Gini index of the Pareto distribution, their exact distributions and moments. These MLEs provide interesting examples of, how random variables which are neither of discrete type nor of continuous type, arise naturally. All these estimators are strongly consistent and they converge in the k-th mean for every k. For Lorenz curve, the asymptotic sampling distribution is lognormal and for Gini index it is normal.
Sankhyā: The Indian Journal of Statistics, Series B (1960-2002) © 1985 Indian Statistical Institute