A General Method for Creating Lorenz Curves

A general method to construct parametric Lorenz models of the weighted‐product form is offered in this paper. Initially, a general result to describe the conditions for the weighted‐product model to be a Lorenz curve, created by using several component parametric Lorenz models, is given. We show that the key property for an ideal component model is that the ratio between its second derivative and its first derivative is increasing. Then, a set of Lorenz models, consisting of a basic group of models, along with their convex combinations, is proposed, and it is shown that any model in the set possesses this key property. We introduce the concept of balanced fit, which provides a means of assigning weights, according to the preferences of the practitioner, to two alternative objectives for developing Lorenz curves in practice. These objectives are generating an acceptable Lorenz curve and improving the accuracy of the density estimation. We apply the balanced fit approach to income survey data from China to illustrate the performance of our models. We first show that our models outperform other popular traditional Lorenz models in the literature. Second, we compare the results generated by the balanced fit approach applied to one of the Lorenz models that we develop with those generated by the kernel method to show that the approach proposed in the paper generates plausible density estimates.