Influence function-based empirical likelihood and generalized confidence intervals for the Lorenz curve

  • Yuyin Shi
  • Bing Liu
  • Gengsheng QinEmail author
Original Paper


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.


Empirical likelihood Influence function Generalized pivotal quantities The Lorenz curve 



The authors are thankful to the anonymous referees for their helpful suggestions and comments.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsGeorgia State UniversityAtlantaUSA

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