First applications of a new three-parameter distribution for non-negative variables

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First applications of a new three-parameter distribution for non-negative variables

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journal	STATISTICA & APPLICAZIONI
issue	STATISTICA & APPLICAZIONI - 2012 - 2
title	First applications of a new three-parameter distribution for non-negative variables
authors	Leo Pasquazzi Mariangela Zenga Michele Zenga
publisher	Vita e Pensiero
format	Article \| Pdf
online since	02-2012
issn	18246672 (print)
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Description Readers' comments
SUMMARY 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. In this paper we explore some methods for fitting the new density to empirical income distributions. We will see that D’Addario’s invariants method clearly outperforms Pearson’s moments method, which does not seem to work well with heavy tailed distributions. Further, we propose some new methods based on the minimization of a measure for the goodness of fit, imposing restrictions on the parameter space to preserve some features of the empirical distribution in the fitted model. We will see that these methods provide very satisfactory results with income distributions from Italy, Swiss, US and UK. Keywords: Income Distribution, Zenga’s Distribution, Goodness of Fit, Moments Method, Invariants Method. Enter a comment for First applications of a new three-parameter distribution for non-negative variables

Description Readers' comments

SUMMARY
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. In this paper we explore some methods for fitting the new density to empirical income distributions. We will see that D’Addario’s invariants method clearly outperforms Pearson’s moments method, which does not seem to work well with heavy tailed distributions. Further, we propose some new methods based on the minimization of a measure for the goodness of fit, imposing restrictions on the parameter space to preserve some features of the empirical distribution in the fitted model. We will see that these methods provide very satisfactory results with income distributions from Italy, Swiss, US and UK.

Keywords: Income Distribution, Zenga’s Distribution, Goodness of Fit, Moments Method, Invariants Method.

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