Recurrence relations for moments of different orders of extremes from gamma distribution

Certain recurrence relations for the moments of different orders of the largest order statistic from a gamma distribution with shape parameter p are obtained. By using this it is shown that for obtaining the moment of any order of each order statistic of a sample of size n from the gamma distribution, one has to evaluate at most n-2 single integrals.     

On unbiased estimation of gini index and yntema-pietra index of lognormal distribution and their variances

Here we derive the uniformly minimum variance unbiased (best) estimator and a strongly consistent, asymptotically normal, unbiased estimator of each of Gini index and Yntema-Pietra index of lognormal distribution . These estimators are in terms of generalized hypergeometric functions ₁F₂. Further, the variances of these estimators and the best estimators of variances of best estimators are found out. They are in terms of Kempé de Fériet's hypergeometric functions.