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.