Date of Award


Degree Type


Degree Name

Master of Science (MS)


Mathematics and Statistics

First Advisor

Dr. Gengsheng (Jeff) Qin - Chair

Second Advisor

Dr. Xu Zhang

Third Advisor

Dr. Pulak Ghosh

Fourth Advisor

Dr. Yu-Sheng Hsu


Lorenz curves are extensively used in economics to analyze income inequality metrics. In this thesis, we discuss confidence interval estimation methods for generalized Lorenz curve. We first obtain normal approximation (NA) and empirical likelihood (EL) based confidence intervals for generalized Lorenz curves. Then we perform simulation studies to compare coverage probabilities and lengths of the proposed EL-based confidence interval with the NA-based confidence interval for generalized Lorenz curve. Simulation results show that the EL-based confidence intervals have better coverage probabilities and shorter lengths than the NA-based intervals at 100p-th percentiles when p is greater than 0.50. Finally, two real examples on income are used to evaluate the applicability of these methods: the first example is the 2001 income data from the Panel Study of Income Dynamics (PSID) and the second example makes use of households’ median income for the USA by counties for the years 1999 and 2006


Included in

Mathematics Commons