Inequality measurement based on grouped data is usually performed by non-linear squares. We propose here an alternative approach building on the compositional nature of the shares of income derived from quantiles. Three parametric Lorenz curves are estimated after trasforming the income shares with the isometric logratio transform. The performance of our simplicial approach is then compared by means of a Monte Carlo Experiment with the methodology proposed by Chotikapanich and Griffiths (2002) based on the Dirichlet distribution and with the non-linear squares. To this purpose, the resulting bias in the Gini coefficient associated with the estimated curves is evaluated across increasing quantiles and different income distributions.