A hybrid method for creating Lorenz curves

We first suggest a bi-parametric Lorenz curve and then analyze the curvature structure of the function. We then build a series of single-parameter Lorenz curves with varied curvatures, which are special cases of the rational function. A hybrid method is then introduced for creating efficient functional models for the Lorenz curve from the single-parameter functional forms. Using grouped income distribution data for the United States, we find that our proposed models perform well.