Minimum sample sizes in asymptotic confidence intervals for Gini’s inequality measure
by Francesca Greselin, Leo Pasquazzi
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.
A Subgroups Decomposition of Zenga’s Uniformity and Inequality indexes
by Paolo Radaelli
We propose a subgroups decomposition of the uniformity index recently introduced by Zenga
. The decomposition scheme adopted follows the structure of the index which is based on the
ratios between lower and upper arithmetic means. The keypoint is the evaluation of the point uniformity
index both within the same subgroup and between two different subgroups. The decomposition
obtained for the uniformity index is finally applied to achieve an analogous decomposition of the
The continuous random variable with uniform point inequality measure
by Marcella Polisicchio
By using the conditions that the expected value of an absolute random variable X is finite and positive
and that the point inequality measure I ðpÞ is uniform for 0 < p < 1, this paper discusses the
question of the existence of such random variable and proves that this problem has a unique solution.
The obtained cumulative distribution function of X is a truncated Pareto distribution, with traditional
inequality parameter equal to 0,5 and with support depending on the finite and positive expected
value and the level of uniformity, based on the ratios between the lower means and the
upper means, used for defining the point inequality measure I(p).
A symbolic data approach for missing values treatment in principal component analysis
by Paola Zuccolotto
There are two ways in order to completely perform a Principal Component Analysis over a data table
with missing values: somehow imputating values to the missing data or excluding some part of
the original sample from the analysis. Both these solutions can be rather costly, expecially with datasets
having an appreciable number of missing values, but only one or at most two missing on any
particular observational unit. An alternative proposal is formulated in this paper using the concept
of Symbolic Data.
Estimation of power function distribution with application to ecological relative abundance
by R.A. Muhaidat, H. Beldjillali, N.A. Al-Odat, Mohd T. Alodat
In this paper we derive Bayesian and non-Bayesian estimators for the parameter of the power function
distribution, and prediction intervals for the maximum of a future sample. We apply our approach
to field data of plant species relative abundance, the abundance of a given species divided
by the total abundance of all plant species in given a community, collected in a biodiversity project
in central Europe.
Measuring loan recovery rate: methodology and empirical evidence
by Michele Zenga, Raffaella Calabrese
This paper aims at proposing a new methodology to compute recovery rate on non-performing bank
loans, in order to confine this variable within the interval [0,1]. Such a methodology is then applied
to data on loans gathered by the Bank of Italy and some interesting characteristics of the loan recovery
process in the Italian banking market are highlighted. The combined effects of some variables
on the recovery rates are also analysed. In particular, the presence of either collateral or personal
guarantee, the borrower’s residence area are considered, thereby emphasizing the relationship
between the recovery rate and the total exposure.
A definition of neighborhoods based on Local Labor Systems: a regional application on employment data
by Gian Pietro Zaccomer, Pamela Mason
The singling out of a neighborhood is often a critical point when we wish to employ one of the tools
proposed by spatial statistics. In fact this is directly correlated to the researcher’s hypothesis on
how interactions among territorial units affect the performances of the phenomenon under examination.
The aim of this article is to compare results obtained by different shift-share decompositions
related to the annual variation of regional employment in Friuli Venezia Giulia. Many of the different
spatial weights matrices proposed by literature are here taken into consideration. As in other
contexts, in this paper the interpretation of neighborhood is fundamental. Therefore, we introduce a
specific method to create a neighborhood in order to assign it an explicit territorial meaning.
STATISTICA & APPLICAZIONI, VOL. IV, Numero Speciale 2, 2006
We regret a mispelling error of the author name Kadarmanto on the cover page, table
of contents and Editorial (page 3). Our apologies to the author.