the chi-square statistic as an income inequality index

This article presents a novel concept known as the chi-square inequality index, developed through the utilization of the chi-square distance function. the study delves into the essential characteristics necessary for an effective inequality index. additionally, a detailed formulation for the chi-square inequality curve is provided within key inequality models. a comparative analysis between the chi-square curve and the conventional lorenz curve is conducted. furthermore, a stochastic order based on the chi-square inequality curve is introduced. the research includes a simulation analysis to explore the statistical properties of the proposed sampling estimator. to conclude, the article highlights the effectiveness of this index through an application to real-world data.