Sampling Distribution of the Gini Index from a Skew Normal

The Gini concentration ratio has been extensively used in the study of "inequality" of distributions. According to Chakrabarthy (1982), "the Lorenz curve and the Gini index have remained the most popular and powerful tool in the analyses of size distribution of income". A major statistical limitation of Gini Concentration Ratio is the absence and the intractability of appropriate sampling distribution (Hart, 1971, Nigard Sandstrom, 1981) We find that the exact sampling distribution of the Gini Concentration Index for a sample from a Skew Normal population has an Extended Skew Normal distribution. This result can be easily particularized to the normal case.