Revisiting the ordered family of Lorenz curves

Sarabia et al. (1999) present a basic model to create ordered families of Lorenz curves, along with basic theorems that describe the conditions for the models to satisfy the definition of the Lorenz curve. Using these basic models, they suggest a family which includes several well-known Lorenz models as special cases. This paper first shows that their basic theorems can be generalized. The paper then proceeds to propose additional families of Lorenz models. Finally the performance of some of the models is compared and it is shown that more efficient Lorenz models are possible with the assistance of our generalized result of the Sarabia et al. (1999) basic model.