On the parameters of Zenga distribution

In 2010 Zenga introduced a new three parameter model for distributions by size which can be used to represent income, wealth, nancial and actuarial variables. In this paper a summary of its main properties is proposed. After that the article focuses on the interpretation of the parameters in term of inequality. The scale parameter is equal to the expectation, and it does not a ect the inequality, while the two shape parameters and are an inverse and a direct inequality indicators respectively. This result is obtained through stochastic orders based on inequality curves. A procedure to generate random sample from Zenga distribution is also proposed. The second part of the article is about the parameter estimation. Analytical solution of method of moments estimators is obtained. This result is used as starting point of numerical procedures to obtain maximum likelihood estimates both on ungrouped and grouped data. In the application, three empirical income distributions are considered and the aforementioned estimates are evaluated.