Decomposition of Zenga’s inequality index I

This paper concerns some notes about the inequality index based on the ratios between lower and upper arithmetic means recently proposed by Zenga [2006]. Beside some definitions and notation given in section 2, we show (section 3) that the inequality measure proposed fulfills the population replication principle. In the remainder of the paper our purpose is to consider a population partitioned in c subgroups. In this case usually the common aim is to evaluate the within and between subgroups contributions to the overall uniformity (inequality). The first decomposition, derived in section 4, allows to evaluate the contribution of each subgroup to the overall uniformity, this contribution comprises both the within and the between sources. The key point of the main decomposition of the overall uniformity proposed in section 5 is the introduction of the uniformity point index (5.1) which can be evaluated either within the same subgroup or between two different subgroups such that a within/between subgroups uniformity decomposition arises.