  A Lorenz curve is a graphical representation of the distribution of income or
wealth within a population. The generalized Lorenz curve can be created by
scaling the values on the vertical axis of a Lorenz curve by the average output
of the distribution. In this paper, we propose two non-parametric methods for
testing the equality of two generalized Lorenz curves. Both methods are based
on empirical likelihood and utilize a U-statistic. We derive the limiting
distribution of the likelihood ratio, which is shown to follow a chi-squared
distribution with one degree of freedom. We performed simulations to evaluate
how well the proposed methods perform compared to an existing method, by
examining their Type I error rates and power across different sample sizes and
distribution assumptions. Our results show that the proposed methods exhibit
superior performance in finite samples, particularly in small sample sizes, and
are robust across various scenarios. Finally, we use real-world data to
illustrate the methods of testing two generalized Lorenz curves.
