This paper aims to solve confidence interval estimation problems for the Lorenz curve. First, we propose new nonparametric confidence intervals using the influence function-based empirical likelihood method. We show that the limiting distributions of the empirical log-likelihood ratio statistics for the Lorenz ordinates are standard chi-square distributions. We also develop “exact” parametric intervals for the Lorenz ordinate based on generalized pivotal quantities when the underlying income distribution is a Pareto distribution or a Lognormal distribution. Extensive simulation studies are conducted to evaluate the finite sample performances of the proposed methods. Finally, we apply our methods to a real income dataset.

本文旨在解决Lorenz曲线的置信区间估计问题。首先，我们使用基于影响函数的经验似然方法提出新的非参数置信区间。我们表明，洛伦兹纵坐标的经验对数似然比统计的极限分布是标准卡方分布。当基础收入分布是帕累托分布或对数正态分布时，我们还基于广义枢轴数量为Lorenz坐标开发“精确”参数区间。进行了广泛的仿真研究，以评估所提出方法的有限样本性能。最后，我们将我们的方法应用于实际收入数据集。