Sampling distribution of Gini's index of diversity

摘要

In the case of a multinomial distribution Π1(1-Π1)+Π2(1-Π2)+…+ Πk(1-Πk) is at times referred to as Gini's index of diversity. In this paper, we present the distributional properties of the statistic , based on samples of size n for a homogeneous multinomial distribution. For 2≤n≤ 12 and 2≤k≤12, we give a short table of the pdf, cdf, and the moments of D. For large values of n, we mention some results for the asymptotic distribution of D for the general multinomial distribution.