Abstract
Gini index, which is derived from the Lorenz curve of income inequality and shows income inequality in different populations, can be applied to ranking and selectionpopulations. Many procedures are available for ordering and ranking income distributions where the ordering is not linear. However, the researchers often are not interested in ordering the populations but selecting the best (or worst) of available populations indicating a lower (or higher) level of disparities in incomes within the population. Madhuri S. Mulekar (2005) discussed the estimation of overlap ofincome distributions and selection in terms of Gini Measure of income inequality. In this paper, we simulate populations ranking and selection based on Gini index of income inequality for case that the variances are equal but known in income distributions and for case that the variances are unequal but known in income distributions.
Highlights
There are many different numerical measures, such as Gini coefficient (Soltow,1971), coefficient of variation (Braun, 1988), Theil index (Theil, 1967), Atkinson ratio(Atkinson, 1970), and Nelson ratio (Nelson, 1984) among others, used to express thedegree of inequality or variability in income among the members of a given population.Lorenz curve-based measures seem to be the most popular ones used in practice
The ordered values of inequality measures are denoted by G[1]≤G[2]≤...≤G[k] Selection of the population corresponding to G[k] or any population with income inequality measure equal to is considered as the correct selection (CS)
P*(the desired probability of correct selection) and d* are specified by the experimenter before sampling begins.The experimenter uses experience and judgment in specifying constants (d* p*),.The sample size is an increasing function of p* and a decreasing function of d*
Summary
There are many different numerical measures, such as Gini coefficient (Soltow,1971), coefficient of variation (Braun, 1988), Theil index (Theil, 1967), Atkinson ratio(Atkinson, 1970), and Nelson ratio (Nelson, 1984) among others, used to express thedegree of inequality or variability in income among the members of a given population.Lorenz curve-based measures seem to be the most popular ones used in practice. Karoly (1990) compared inequality in individual wage and salary income for years 1967to 1986 using ten different inequality measures including Gini index and estimatedvariances of eight out of ten measures. We simulateprocedure method for selecting a population based on Gini coefficient and obtainoptimal sample size needed to makesuch a selection. SciPress applies the CC-BY 4.0 license to works we publish: https://creativecommons.org/licenses/by/4.0/
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