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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: Springer on behalf of the Indian Statistical Institute
Stable URL: http://www.jstor.org/stable/25052395
Page Count: 12
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Sampling Distributions of Lorenz Curve and Gini Index of the Pareto Distribution
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Abstract

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.

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