In this paper, we investigate the properties of a family of inequality measures which extends the Atkinson indices and is axiomatically characterized by amultiplicative decomposition property, where the within-group component is a generalized weighted mean with weights summing exactly to 1.

This family contains canonical forms of all aggregative inequality measures; each bounded above by 1, has a usefuland intuitive geometric interpretation and provides an alternative dominance criterion for ordering distributions in terms of inequality.

Taking the Spanish Household Budget Surveys (HBS) for 1973/74, 1980/81 and 1990/91 and the morerecent continuous HBS for 2003, we show the advantages and possibilities of this extended family inregard to completing and detailing information instudies of inequality focussing on the tails of the distribution and on the changes in the distribution when the population is partitioned into population subgroups.