Abstract
In the present paper we derived, with direct method, the exact expressions for the sampling probability density function of the Gini concentration ratio for samples from a uniform population of size n = 6, 7, 8, 9 and 10. Moreover, we found some regularities of such distributions valid for any sample size.
Highlights
In 1914 Corrado Gini [1] introduced the concentration ratio R for the measure of inequality among values of a frequency distribution
The Gini index is widely used in fields as diverse as sociology, health science, engineering, and in particular, economics to measure the inequality of income distribution
In 1971 Girone [12] obtained, with direct method, the sampling distribution function of the Gini ratio for samples of size n ≤ 5 drawn from a uniform population
Summary
In 1914 Corrado Gini [1] introduced the concentration ratio R for the measure of inequality among values of a frequency distribution. They showed that these estimators are strongly consistent for the Gini index. Girone (1968) [10] focused on the study of the sampling distribution of the Gini index and in 1971 [11] derived the exact expression for samples drawn from an exponential population. In 1971 Girone [12] obtained, with direct method, the sampling distribution function of the Gini ratio for samples of size n ≤ 5 drawn from a uniform population. We calculate the joint p.d.f. of the new n variables and integrating with respect to the average we obtain the joint p.d.f. of the other n ‒ 1 variables One of these variables is transformed in the concentration ratio. (Section 8), we find some regularities of such distributions valid for any sample size
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