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

digital

Article

Magazine

STATISTICA & APPLICAZIONI

Section

Open Access

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

Pages

Online from

02-2012

Issn

1824-6672 (print) | 2283-6659 (digital)

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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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