Parametric Lorenz curves based on the beta system of distributions

Abstract

Some families of Lorenz curves only approximate specific segments of the income distribution. This potential limitation motivates the consideration of more flexible models, which depart from a convenient form of the Lorenz curve. We begin with a Lorenz curve from which we generate a more flexible family of Lorenz curves through two new parameters. We explore the main properties of this family, including the Lorenz ordering, inequality measures, and Leimkhuler curves. An empirical application with US data suggests that the proposed models fit income data accurately.