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STATISTICA & APPLICAZIONI - 2013 - 1

digital STATISTICA & APPLICAZIONI - 2013 - 1
Digital issue
journal STATISTICA & APPLICAZIONI
issue 1 - 2013
title STATISTICA & APPLICAZIONI - 2013 - 1
publisher Vita e Pensiero
format Digital issue | Pdf
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Contents

Editorial
by Eugenio Brentari pages: 1 Download
Reasons for a translation
by Michele Zenga pages: 1 Download
On the relations between variability indices. Part I
by Gaetano Pietra pages: 16 Download
The confluent hypergeometric-mixture of Polisicchio distributions: a generalized Zenga distribution
by Lucio De Capitani, Alessandro Zini pages: 26 Download
Abstract
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.
Interpreting clusters and their bipolar means: a case study
by Livia Dancelli, Marica Manisera, Marika Vezzoli pages: 14 Download
Abstract
When cluster analysis is performed on ranking or rating data, methods requiring quantitative variables commonly used to characterize the obtained groups, such as the cluster profile plots, are not appropriate. Instead, the bipolar mean, originally introduced in the literature in 2005 to deal with such kind of data, can be useful to interpret the resulting clusters, possibly in association with other available information. An application on real data coming from an extensive survey carried out in 2011 in the Italian McDonald’s restaurants is presented. A selection of ranking data, regarding some features of products and service, was analysed by a hierarchical cluster algorithm. In order to emphasize the concordance between the most important ranks, a weighted rank correlation coefficient was employed to measure the dissimilarity between respondents. Five groups were finally obtained, which show interesting differences on the given rankings.
A longitudinal decomposition of Zenga’s new inequality Index
by Mauro Mussini, Michele Zenga pages: 15 Download
Abstract
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.
Application of Zenga’s distribution to a panel survey on household incomes of European Member States
by Alberto Arcagni, Michele Zenga pages: 24 Download
Abstract
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.
Minimal sample size for testing trinomial proportions for given precision of probability of type I error
by Edyta Mazurek, Katarzyna Ostasiewicz pages: 11 Download
Abstract
The determination of sample size is a common task for many organizational researchers. Inappropriate, inadequate or excessive sample size continues to influence the quality, accuracy and costs of research. Sample size is one of the features of analysis that can influence the detection of significant differences for population so we can’t ignore problem of sample size. This paper presents a procedure and a table for selecting sample size for simultaneously testing the parameters of a trinomial distribution. The results are obtained by examining the several possible value of a trinomial parameter vector and comparing the fixed first error type with the empirical one obtained by building the exact distribution through the code R.

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