Two flexible functional form approaches for approximating the Lorenz curve

This paper introduces two flexible form approaches to approximate Lorenz curves. The first approach expands the inverse function of an income distribution in an exponential polynomial series and derives the Lorenz curve from it. The required convexity condition can be imposed using a Bayesian method. The second approach approximates the Lorenz curve with a sequence of Berstein polynomial functions. The required convexity condition is automatically established in this approach. We compare these approaches with other well-known fixed functional form approaches. We evaluate the performance of these functional forms by comparing approximation errors, maximum error, and the estimates of the Gini coefficient produced by various approaches.