The Distribution of an Index of Dissimilarity for Two Samples from a Uniform Population

Abstract

In this paper the authors study the sample behavior of the Gini’s index of dissimilarity in the case of two samples of equal size drawn from the same uniform population. The paper present the analytical results obtained for the exact dis tribution of the index of dissimilarity for sample sizes n ≤ 8 . This result was obtained by expressing the index of dis similarity as a linear combination of spacings of the pooled sample. The obtained results allow to achieve the exact ex pressions of the moments for any sample size and, therefore, to highlight the main features of the sampling distributions of the index of dissimilarity. The present study can enhance inferential statistical aspects about one of the main contri butions of Gini.