Some properties of the Canberra inequality index

Abstract

In this paper, we study some properties of the Canberra index which is based on Canberra distance function. Some features that required to an inequality index are investigated. Also we present explicit expression for the Canberra curve in some important inequality distributions. Further, we compare the Canberra curve with the traditional Lorenz curve. A simulation study based on fitted distribution to real income data is performed in order to investigate the asymptotic behavior of the proposed sampling estimator. Finally, the superiority of this index is illustrated by means of a real data set.