H-type indices, partial sums and the majorization order

Abstract

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