  The Lorenz curve portrays the inequality of income distribution. In this
article, we develop three modified empirical likelihood (EL) approaches
including adjusted empirical likelihood, transformed empirical likelihood, and
transformed adjusted empirical likelihood to construct confidence intervals for
the generalized Lorenz ordinate. We have shown that the limiting distribution
of the modified EL ratio statistics for the generalized Lorenz ordinate follows
the scaled Chi-Squared distributions with one degree of freedom. The coverage
probabilities and mean lengths of confidence intervals are compared of the
proposed methods with the traditional EL method through simulations under
various scenarios. Finally, the proposed methods are illustrated using a real
data application to construct confidence intervals.
