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STATISTICA & APPLICAZIONI - 2006 - Special issue 1

digital STATISTICA & APPLICAZIONI - 2006 - Special issue 1
Digital issue
journal STATISTICA & APPLICAZIONI
issue Special issue 1 - 2006
title STATISTICA & APPLICAZIONI - 2006 - Special issue 1
publisher Vita e Pensiero
format Digital issue | Pdf
language English
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Primo numero speciale del 2006

EDITORIAL

Editorial
by Achille Lemmi, Michele Zenga pages: 3 Download
Abstract
This special issue of Statistica & Applicazioni provides a selection of papers, which were presented and discussed at the International Conference to Honor Two Eminent Social Scientists. Dedicated to the memory of Corrado Gini and Max Otto Lorenz, the conference highlighted how remarkable and permanent is their seminal contribution in research carried out by the community of scholars in the last century. It was held in May 2005 at the Certosa di Pontignano of Siena University, following the initiative of Professors Camilo Dagum and Samuel Kotz.

CONTENTS

Escaping poverty in Spain: 1993-2000. What are the main routes?
by Elena Bárcena Martín, Antonio Fernández Morales, Beatriz Lacomba Arias, Guillermina Martín Reyes pages: 25 Download
Abstract
This paper investigates the effects of different events on the probability of escaping poverty in Spain. We first use a mutually exclusive hierarchical categorization of event types for each person experiencing a poverty spell ending and find that demographic events occur in 16% of households transiting out of poverty while income events occur in 84% remaining cases. Once we decompose the effects of trigger events in the prevalence of events and differences in the chances of making a transition conditional on an event we find that the routes out of poverty are varied. Wage and salary earnings events take place more often and are quite effective in the promotion of households out of poverty, while the welfare state events are less frequent but can be more effective. Multivariate results corroborate that there are factors that reduce chances to escape poverty: time spent in poverty, pensions or unemployment as main household income and certain situation and types of households. On the other hand, the most effective increment is in wage and salary earnings or self-employment and the higher the number of active members or income receiver members in the household, the higher the chances to leave poverty.
Keywords: trigger events, exits from poverty, hierarchical categorization, multivariate regression.
Some developments about a new nonparametric test based on Gini’s mean difference
by Claudio Giovanni Borroni, Manuela Cazzaro pages: 14 Download
Abstract
In this paper the performance of a new nonparametric test proposed by Borroni and Zenga (2003) for the independence of two criteria is discussed. The test-statistic is based on Gini’s mean difference computed on the total ranks assigned to each sampled unit according to the chosen criteria of sorting. The performance of the test is measured by simulating its power function via Monte Carlo methods when it is applied as a one-sided test of independence against concordance. At this aim, after assuming that the two criteria of ranking are based on the values taken by two quantitative variables, a wide range of bivariate models is set for the two populations. The choice of the simulated models reflects the common situation of sampling from non-Normal populations, usually faced in economic applications. The reported results show that the new proposed test has often good performances and can be considered as a natural competitor of other common nonparametric tests.

Keywords: nonparametric tests, rank correlation indexes, Gini’s mean difference, Monte Carlo simulations.
Exact Distribution of the Gini Concentration Index from a Skew-Normal Sample
by Corrado Crocetta, Nicola Loperfido pages: 7 Download
Abstract
The skew-normal distribution and the fundamental skew-normal distribution are two generalizations of the normal one. The former can model moderate skewness and kurtosis, while the latter is very useful when dealing with ordering constraints. In this paper we demonstrate that the exact sampling distribution of the Gini Concentration Index from a skew-normal is a fundamental skew-normal distribution. Implications of this result are twofold. In the first place, it easily applies to the case of sampling from a normal distribution, which can be regarded as a skew-normal distribution with shape parameter equal to zero. In the second place, the result can be easily generalized to other measures of inequality which can be represented as ratios of linear combinations of order statistics. The paper also recalls some relevant properties of the skew-normal distributions and motivates its use in statistical modelling.

Keywords: Skew-Normal, L-statistics, Small Sample, Gini Concentration Ratio, Exact Distribution.
A new Q-Q plot and its application to income data
by Agostino Tarsitano pages: 19 Download
Abstract
A common practice to analyze income data is to fit a model to data and then compute all the inequality indices that appear useful as functions of the estimated shape parameters. In a sense, the choice of the probability distribution and the choice of the inequality index are independent. This paper develops a technique, based on Q-Q plot, that is useful for the identification of both the model for the size distribution of incomes and the measure of economic inequality.

Keywords: order statistics, direct search estimates, correlation coefficient, simulation.
On the construction of fuzzy measures for the analysis of poverty and social exclusion
by Gianni Betti, Bruno Cheli, Achille Lemmi, Vijay Verma pages: 21 Download
Abstract
This paper is a contribution to the analysis of deprivation seen as a multi-dimensional condition. Multi-dimensionality involves both monetary and diverse non-monetary aspects – the former as the incidence and intensity of low income, and the latter as a lack of access to other resources, facilities, social interactions and even individual attributes determining the life-style. A most useful tool for such analysis is to view deprivation as a matter of degree, giving a quantitative expression to its intensity for individuals in different dimensions and at different times. Such ‘fuzzy’ conceptualisation has been increasingly utilised in poverty and deprivation research. This paper aims to further develop and refine this strand of research, so as to integrate it in the form of a more ‘integrated fuzzy and relative’ (IFR) approach to the analysis of poverty and deprivation. The concern of the paper is primarily methodological rather than detailed numerical analysis from particular applications. We re-examine the two additional aspects introduced by the use of fuzzy (as distinct from the conventional poor/non-poor dichotomous) measures, namely: the choice of membership functions and the choice of rules for the manipulation of the resulting fuzzy sets, rules defining their complement, intersection, union and averaging. The relationship of the proposed fuzzy monetary measure with the Lorenz curve and the Gini coefficient.

Keywords: income poverty, multidimensional deprivation, fuzzy set operators.
Convergence of the Sample Mean Difference to the normal distribution: simulation results
by Francesca Greselin, Michele Zenga pages: 24
Abstract
The present work aims to obtain the value of minimum sample size required by a good approximation by the normal curve for the sample mean difference. Particular care is given to what happens in the tails of the curves, with the aim of deriving confidence intervals for Gini’s mean difference. This goal is obtained by empirical methods and the presented results have an explorative nature. Simulation data have been obtained sampling from different distributions, considering symmetry versus asymmetry and the existence of the moments as main aspects in the underlying distribution. These remarks lead to the choice of the normal, the rectangular, the exponential and the Pareto distributions. All the obtained results indicate that the shape of the distribution from which the samples are generated is critically related to the minimum sample sizes required for a good approximation of the tails of the sample mean difference to the normal curve.

Keywords: Gini Mean Difference, asymptotic distribution, convergence, U-statistic.
Convergence of the Sample Mean Difference to the normal distribution: simulation results
by Francesca Greselin, Michele Zenga pages: 24 Download
Abstract
The present work aims to obtain the value of minimum sample size required by a good approximation by the normal curve for the sample mean difference. Particular care is given to what happens in the tails of the curves, with the aim of deriving confidence intervals for Gini’s mean difference. This goal is obtained by empirical methods and the presented results have an explorative nature. Simulation data have been obtained sampling from different distributions, considering symmetry versus asymmetry and the existence of the moments as main aspects in the underlying distribution. These remarks lead to the choice of the normal, the rectangular, the exponential and the Pareto distributions. All the obtained results indicate that the shape of the distribution from which the samples are generated is critically related to the minimum sample sizes required for a good approximation of the tails of the sample mean difference to the normal curve.

Keywords: Gini Mean Difference, asymptotic distribution, convergence, U-statistic.
Binary segmentation methods based on Gini index: a new approach to the multidimensional analysis of income inequalities
by Michele Costa, Giuliano Galimberti, Angela Montanari pages: 19 Download
Abstract
The role of individual covariates in explaining income differences and poverty structure has been deeply analyzed in the literature.
In this paper we propose to study the effect of socio-demographic and geographical characteristics on subgroup differences by developing a non parametric regression model for income inequalities, based on recursive partitioning methods. Within the philosophy of Classification and Regression Trees we suggest to replace the usually employed splitting criterion, based on the well known decomposition into between and within group deviance components, with a new criterion based on Gini index, which minimizes inequality within subgroups. This solution allows to better detect the covariates which mainly influence income inequality by taking into account all the income distributional aspects and points out specific income profiles.

Keywords: regression trees, Gini inequality index, Gini index decomposition.