This thesis aims to solve confidence interval estimation problems for Lorenz curve. First, we propose new nonparametric confidence intervals with influence function-based empirical likelihood method. It is shown that the limiting distributions of log-empirical likelihood ratios are standard Chi-square distributions. Then the ``exact'' parametric intervals based on generalized pivotal quantities for Lorenz ordinates are also developed. Extensive simulation studies are conducted to evaluate the finite sample performance of the proposed methods. Finally, our methods are applied on real income data sets.