On Zenga and Bonferroni curves

Abstract

Three alternative inequality curves are considered as competitors of the classical Lorenz curve as descriptors of income inequality. The Bonferroni curve and the Zenga-07 curve appear to be essentially equivalent to the Lorenz curve. They each determine the parent distribution up to scale factor, and they each yield an inequality partial order that is equivalent to the Lorenz order. The Zenga-84 curve is more problematic. It is scale invariant, but it is possible that different distributions can have the same Zenga-84 curve. Thus it fails to identify the parent distribution up to a scale factor.