Extending the Lorenz curve to higher dimensions: A multivariate quantile function approach

Real-world inequality often involves multiple attributes such as income, education, and health, necessitating a higher-dimensional approach to inequality measurement. This paper introduces a multivariate Lorenz curve based on multivariate quantile functions, capturing the joint distribution of multiple attributes and providing an interpretable measure of multidimensional inequality. Theoretical properties are explored, its relationship with the multivariate Leimkuhler curve is established, and a statistical analysis is conducted using real-world data. This framework offers a comprehensive tool for studying inequality across various socioeconomic dimensions.