Leo Pasquazzi
Titoli dell'autore
First applications of a new three-parameter distribution for non-negative variables
Gratis
digital
formato:
Articolo
| STATISTICA & APPLICAZIONI - 2012 - 2


Anno:
2012
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.
More on M.M. Zenga’s new three-parameter distribution for nonnegative variables
Gratis
digital
formato:
Articolo
| STATISTICA & APPLICAZIONI - 2011 - 1


Anno:
2011
SUMMARY
Recently Zenga (2010) has proposed a new three-parameter density function f (x : µ; α; θ), (µ > 0;
α > 0; θ > 0), for non-negative variables. The parameter µ is equal to the expectation of the distribution. The new density has positive asymmetry and Paretian right tail. For θ > 1, Zenga (2010) has obtained the expressions of: the distribution function, the moments, the truncated moments, the mean deviation and Zenga’s (2007a) point inequality A(x) at x = µ. In the present paper, as to the general case θ > 0, the expressions of: the distribution function, the ordinary and truncated moments, the mean deviations and Zenga’s point inequality A (µ) are obtained. These expressions are more complex than those previously obtained for θ > 1 by Zenga (2010). The paper is enriched with many graphs of: the density functions (0.5 ≤ θ ≤ 1.5), the Lorenz L(p) and Zenga’s I (p) curves as well as the hazard and survival functions.
Keywords: Non-Negative Variables, Positive Asymmetry, Paretian Right Tail, Beta Function, Lorenz Curve, Zenga’s Inequality Curve, Hazard Function, Survival Function.
Minimum sample sizes in asymptotic confidence intervals for Gini’s inequality measure
Gratis
digital
formato:
Articolo
| STATISTICA & APPLICAZIONI - 2008 - 2


Anno:
2008
Statistical inference for inequality measures has been of considerable interest in recent years. Income
studies often deal with very large samples, hence precision would not seem a serious issue.
Yet, in many empirical studies large standard errors are observed (Maasoumi, 1997). Therefore, it
is important to provide methodologies to assess whether differences in estimates are statistically significant.
This paper presents an analysis of the performance of asymptotic confidence intervals for
Gini’s index, virtually the most widely used inequality index. To determine minimum sample sizes
assuring a given accuracy in confidence intervals, an extensive simulation study has been carried
out. A wide set of underlying distributions has been considered, choosing from specific models for
income data. As expected, the minimum sample sizes are seriously affected by some population
characteristics as tail heaviness and asymmetry. However, in a wide range of cases, it turns out that
they are smaller than sample sizes actually used in social sciences.
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