Robust estimators for Pareto and lognormal distributions in income inequalities evaluation

Considerations related to a nature of allocation of wealth within a populations have a central position in the economics and public debate related to social justice and social solidarity. In this paper we show selected aspects of robust estimation of the income distribution. We focus our attention on two well-known models for the income distribution namely on the Pareto and lognormal distributions and on popular income inequality measures namely on the Lorentz curve and the Gini coefficient. The presented arguments however are applicable to a wide class of over 100 models used for income distributions modelling which are by default estimated by means of maximal likelihood methodology. Our findings can be applied to the robust financial modelling as well. Theoretical considerations are illustrated by means of empirical examples.