Estimating the Three Parameters of Zenga's Distribution for Income by Size
Michele Zenga, Alberto Arcagni
Quantitative Methods for Economics and Business (DIMEQUANT), University of Milano-Bicocca, Milan, Italy

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.

Keywords: Income distribution; Zenga's distribution; Goodness of fit; Moments method

Biography: Education: He graduated in Economics at 'Università Cattolica' of Milan in 1963. He graduated in Statistics at University of Rome in 1967. Academic positions: He qualified in university teaching in Statistics in 1969. He qualified as 'professore straordinario' in Statistics in 1975. He is 'professore ordinario' (full professor) in Statistics since 1978. Main appointments: President, Executive Committee for the Faculty of Economics, University of Trento, 1978. Dean, Faculty of Economics, University of Trento, 1978-80 and 1981-83. Coordinator of 'Dottorato di Ricerca' in Methodological Statistics at University of Trento (of Milano-Bicocca at present) since the first year of institution, academic year 1983/1984. Director, undergraduate studies in Economics and Politics, Faculty of Political Science, University of Milan, 1987-90. Dean, Faculty of Economics, University of Milan (and subsequently of Milano-Bicocca), from academic year 1993/94 to academic year 2001/02. Chair, Department of Quantitative Methods for Economics and Business Sciences, University of Milano-Bicocca, 2003-2009.