In this thesis, an empirical likelihood method based on influence function is developed and used to construct confidence intervals for the Lorenz ordinates. This method is defined under the simple random sampling and the limiting distribution of the proposed empirical likelihood ratio statistic is a standard Chi-square distribution. Extensive simulation studies are conducted to evaluate the proposed empirical likelihood-based confidence intervals for the Lorenz ordinates. Finally, this method is used on a real income data as an application.