An exponential family of Lorenz curves

Abstract

A new method for building parametric-functional families of Lorenz curves, generated from an initial Lorenz curve (which satisfies some regularity conditions), is presented. The method is applied to the exponential family since they use the exponential Lorenz curves as their generating curves. Several properties of these families are analyzed, including the population function, inequality measures, and Lorenz orderings. Finally, an application is presented for data from various countries. The family is shown to perform well in fitting the data across countries. The results are very robust across data sources.