Events and Meetings of Italian Statistical Society, Statistics and Demography: the Legacy of Corrado Gini

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A simplicial approach to inequality measurement
Lisa Crosato, Gianna Serafina Monti

Last modified: 2015-09-05


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.

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