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A Lorenz curve is a graphical representation of the distribution of income orwealth within a population. The generalized Lorenz curve can be created byscaling the values on the vertical axis of a Lorenz curve by the average outputof the distribution. In this paper, we propose two non-parametric methods fortesting the equality of two generalized Lorenz curves. Both methods are basedon empirical likelihood and utilize a U-statistic. We derive the limitingdistribution of the likelihood ratio, which is shown to follow a chi-squareddistribution with one degree of freedom. We performed simulations to evaluatehow well the proposed methods perform compared to an existing method, byexamining their Type I error rates and power across different sample sizes anddistribution assumptions. Our results show that the proposed methods exhibitsuperior performance in finite samples, particularly in small sample sizes, andare robust across various scenarios. Finally, we use real-world data toillustrate the methods of testing two generalized Lorenz curves.

U-Statistics Based Jackknife Empirical Likelihood Tests for the Generalized Lorenz Curves