Measuring economic inequality is a significant and meaningful topic in our social system. The Gini index and Pietra ratio are used by many people, but limited to reflecting the sampling distribution. In this thesis, we studied the interval estimates with another measure called the lower-mean ratio u, which was introduced by Elteto and Frigyes (1968). By using jackknife empirical likelihood (JEL), adjusted jackknife empirical likelihood (AJEL), mean jackknife empirical likelihood (MJEL), mean adjusted jackknife empirical likelihood (MAJEL), and adjusted mean jackknife empirical likelihood (AMJEL) methods, we proposed the interval estimator for u. In the following simulation study, we made a comparison for these methods under different distributions in terms of the coverage probability and the average confidence interval length. The results indicate that MAJEL performs best among these methods for small sample sizes of skewed distribution. For a small sample size of normal distribution, both JEL and MJEL show better performance than the other methods but MJEL is relatively time-consuming. All methods exhibit good performance for a large sample size. The two real data set analyses further illustrate the proposed methods, and the results are consistent with those in the simulation study.