Chotikapanich and Griffiths (Journal of Business and Economic Statistics, 2002, 20(2), 290-295) introduced the Dirichlet distribution to the estimation of Lorenz curves. This distribution naturally accommodates the proportional nature of income share data and the dependence structure between the shares. Chotikapanich and Griffiths fit a family of five Lorenz curves to one year of Swedish and Brazilian income share data using unconstrained maximum likelihood and unconstrained nonlinear least squares. We attempt to replicate the authors' results and extend their analyses using both constrained estimation techniques and five additional years of data. We successfully replicate a majority of the authors' results and find that some of their main qualitative conclusions also hold using our constrained estimators and additional data.