  The Gini index signals only the dispersion of the distribution and is not
very sensitive to income differences at the tails of the distribution. The
widely used index of inequality can be adjusted to also measure distributional
asymmetry by attaching weights to the distances between the Lorenz curve and
the 45-degree line. The measure is equivalent to the Gini if the distribution
is symmetric. The alternative measure of inequality inherits good properties
from the Gini but is more sensitive to changes in the extremes of the income
distribution.
