Parametric Families for the Lorenz Curve: An Analysis of Income Distribution in European Countries

The European Union Survey on Income and Living Conditions (EU-SILC) is the main source of information about living standards and poverty in the EU member states. We compare different parametric models for the Lorenz curve (LC) with an empirical analysis of the income distributions of 26 European countries in the year 2017. The objective of our empirical study is to verify whether simple mono-parametric models for the LCs can represent similarities or differences between European income distributions in sufficient detail, or whether an alternative, more sophisticated multi-parametric model should be used instead. In particular, we consider the power LC, the Pareto LC, the Lamè LC, a generalised bi-parametric version of the Lamè LC, a bi-parametric mixture of power LCs and the recently introduced arctan family of LCs. Whilst the first three families are ordered, in that different parametric values correspond to a situation of Lorenz ordering, the latter three may also identify the ambiguous situation of intersecting LCs. Therefore, besides focusing on the goodness-of-fit of the models considered and their mathematical simplicity, we evaluate the effectiveness of multi-parametric models in identifying the non-dominated cases.