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Decomposition of Zenga’s inequality index by sources
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format: Article | STATISTICA & APPLICAZIONI - 2012 - 1
Year: 2012
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More on M.M. Zenga’s new three-parameter distribution for nonnegative variables
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digital
format: Article | STATISTICA & APPLICAZIONI - 2011 - 1
Year: 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.
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Application of Zenga’s distribution to a panel survey on household incomes of European Member States
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digital
format: Article | STATISTICA & APPLICAZIONI - 2013 - 1
Year: 2013
In this paper Zenga’s distribution is applied to 114 household incomes distributions from a panel survey conducted by Eurostat. Previous works showed the good behaviour of the model to describe income distributions and analyzed the possibility to impose restrictions on the parametric space so that the fitted models comply with some characteristics of interest of the samples. This work is the first application of the model on a wide number of distributions, showing that it can be used to describe incomes distributions of several countries. Maximum likelihood method on grouped data and methods based on the minimization of three different goodness of fit indexes are used to estimate parameters. The restriction that imposes the equivalence between the sample mean and the expected value of the fitted model is also considered. It results that the restriction should be used and the changes in fitting are analyzed in order to suggest which estimation method use jointly to the restriction. A final section is devoted to the direct proof that Zenga’s distribution has Paretian right-tail.
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A longitudinal decomposition of Zenga’s new inequality Index
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digital
format: Article | STATISTICA & APPLICAZIONI - 2013 - 1
Year: 2013
The paper proposes a three-term decomposition of Zenga’s new inequality index over time. Given an initial and a final time, the link among inequality trend, re-ranking, and income growth is explained by decomposing the inequality index at the final time into three components: one measuring the effect of re-ranking between individuals, a second term gauging the effect of disproportional growth between individuals’ incomes, and a third component measuring the impact of the inequality existing at the initial time. The decomposition allows one to distinguish the determinants of inequality change from the contribution of the inequality at the initial time to the inequality at the final time. We applied the decomposition to Italian household income data collected by the Survey on Household Income and Wealth of the Bank of Italy, waves 2008-2010.
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Some remarks on Zenga’s approach to kurtosis digital
format: Article | STATISTICA & APPLICAZIONI - 2016 - 2
Year: 2016
In this paper, several insights on the Zenga’s approach for the measurement of Kurtosis are provided. These insights mainly regard the connections between Kurtosis and Concentration indexes and the relation between the Kurtosis diagram and an extension of the well-known Lorenz curve, i.e. the relative first incomplete moment function...
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Joint decomposition by subpopulations and sources of the Zenga inequality index I(Y) digital
format: Article | STATISTICA & APPLICAZIONI - 2015 - 2
Year: 2015
Keywords: Zenga Inequality Index, Income Inequality, Joint Decomposition by Subpopulations and Sources, Point and Synthetic Inequality Indexes.
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Decomposition by sources of the Gini, Bonferroni and Zenga inequality indexes digital
format: Article | STATISTICA & APPLICAZIONI - 2013 - 2
Year: 2014
Keywords: Inequality, Scale Transformation Matrix, Point Inequality Index, Decomposition...
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Zenga distribution: parameters estimation with constraints on synthetic inequality indices digital
format: Article | STATISTICA & APPLICAZIONI - 2014 - 1
Year: 2015
In 2010, Zenga introduced a three-parameter model for distributions by size, with Paretian right-tail and expectation always finite...
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First applications of a new three-parameter distribution for non-negative variables
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digital
format: Article | STATISTICA & APPLICAZIONI - 2012 - 2
Year: 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.
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Asymptotic properties of some estimators for Gini and Zenga inequality measures: a simulation study digital
format: Article | STATISTICA & APPLICAZIONI - 2015 - 2
Year: 2015
It is well known that unequal income distribution, yielding poverty, stratification and polarization, can be a serious economic and social problem. The reliable inequality analysis of both, total population of households and subpopulations classified by different characteristics, can be a helpful piece of information for economists and social policy- makers. Therefore, it seems especially important to present reliable estimates of income inequality measures for a population of households in different divisions...
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A comparison among two generalized beta-mixtures of polisicchio distributions and the zenga model digital
format: Article | STATISTICA & APPLICAZIONI - 2013 - 2
Year: 2014
In this paper, the performances in fitting incomes of three different mixtures of Polisicchio distributions are compared...
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The confluent hypergeometric-mixture of Polisicchio distributions: a generalized Zenga distribution
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digital
format: Article | STATISTICA & APPLICAZIONI - 2013 - 1
Year: 2013
We propose a generalization of the three-parameters Zenga distribution obtaining a four-parameters model. The generalization is performed using the confluent hypergeometric distribution as mixing distributions in place of the classical beta. We compare the flexibility of the resulting model with that of the Zenga distribution observing some improvements.
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