Estimating the three parameters of Zenga's distribution for income by size

M.M. Zenga (2010a) recently proposed a new three-parameter family of density functions for non-negative variables. Its properties resemble those of economic size distributions: it has positive asymmetry, Paretian right tail and it may be zeromodal, unimodal or even bimodal. One of the parameters is equal to the expected value and the other two are inequality indicators. In this work we considered several methods of fitting the new density to empirical distributions and we studied the properties of the resulting estimators. The methods we considered are the method of moments and methods based on minimization of goodness-of-fit indexes. These indexes are obtained as different types of means of relative distances between observed and theoretical frequencies which depend on the model parameters. Minimization methods have been implemented both without restrictions and with restrictions on statistics that are considered of interest to describe income distributions. These statistics are the arithmetic mean and inequality indexes such as Pietra index and Zenga's point inequality index (Zenga 2007). The analysis of the distributions of the estimators and goodness-of-fit indexes has been conducted by Monte Carlo methods.