Application of Zenga's distribution to a panel survey on household incomes of 15 European Member States

Zenga’s distribution is particularly suitable for modelling income distributions since it is positively skewed and it has Paretian right tail. This new density has three parameters: a scale parameter, which is equal to the expected value, and two shape parameters which affect the inequality. At the 58th ISI World Statistic Congress Zenga and Arcagni (2011) have presented an application on 114 empirical income distributions from European Community Hosehold Panel. Parameters estimates were obtained by method of moments and by minimizing goodness of fit indexes. These methods were implemented both without and with restrictions on the expected value and on punctual inequality indexes. In this work, the application is extended with the maximum likelihood parameters estimation, considering both the unrestricted model and the model with restriction on the expected value. Since global inequality indexes of the model have to be evaluated numerically, the parameter estimation with the restriction on these indexes can be complicated. A proposal on how to impose this kind of restrictions is provided.