h-Type indices, partial sums and the majorization order

We study the array of partial sums, P X , of a given array X in terms of its h-type indices. Concretely, we show that h( P X ) can be described in terms of the Lorenz curve of the array X and obtain a relation between the sum of the components of P X and the Gini index of X. Moreover, we obtain sharp lower and upper bounds for h-type indices of P X...