Abstract
The similarities and dissimilarities among incomes of two or more groups are studied using several different measures. Two of such measures, one overlap-based and one distance-based are studied here. Weitzman (1970) introduced coefficient of community to study income distributions of different social groups in the United States. However, this study involved no distributional assumption about the incomes of families in different groups. Because, the classical Pareto law has proven to be a convenient model to describe income distributions, a continuous counterpart of coefficient of community and a variation of Hellinger’s distance are developed to study income equalities under the assumption of Pareto model. The estimators of both the measures are found to be biased, and hence the expressions are derived for evaluating the amount of bias in estimates. The mean squared errors and bias of estimates are studied using Monte Carlo technique for different sample sizes.
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Mulekar, M.S., Fukasawa, T. Estimation of Statistical Measures of Income Similarity. J Stat Theory Pract 4, 743–755 (2010). https://doi.org/10.1080/15598608.2010.10412016
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DOI: https://doi.org/10.1080/15598608.2010.10412016