Novel credibility approaches for Lorenz curve and Gini coefficient estimation

Abstract

The Lorenz curve and Gini coefficient are prominent statistical tools used in various fields to measure income inequality, wealth distribution, and other distributions of resources within a population. However, traditional estimations of Lorenz curve and Gini coefficient often overlook the utilization of prior information, relying solely on sample data. This paper adopts credibility theory principles to propose a novel approach, combining empirical and collective Lorenz curves through weighted estimation. By optimizing these weights under the integral square loss function, the study derives two credibility estimations for the Lorenz curve and Gini coefficient. Asymptotic properties of these estimations are established, and numerical simulations validate the comparison of their small-sample properties with traditional methods.