# Vita e Pensiero

Estimation of the variance for logistic distribution under ranked set sampling and simple random sampling: a comparative study

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digital
Year:
2012

SUMMARY
The logistic distribution is applicable in many area of research. In this study, several estimators of
the variance when the location parameter is known and unknown are considered when data are
gathered under simple random sampling (SRS) and ranked set sampling (RSS). For some estimators
considered, the bias and mean square error (MSE) are not gotten in closed form. Using Monte Carlo
simulations, comparison of these estimators is made based on biases, MSE and efficiency. When
the estimators are compared, it is found that estimators based on maximum likelihood method are
more efficient than other estimators considered, under both SRS and RSS. However, estimators
based on RSS have more advantages over those based on SRS.
Keywords: Logistic Distribution, Ranked set Sampling, Simple Random Sampling, Variance, Estimations.

Regression model for proportions with probability masses at zero and one

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digital
Year:
2012

SUMMARY
In many settings, the variable of interest is a proportion with high concentration of data at the
boundaries. This paper proposes a regression model for a fractional variable with nontrivial probability
masses at the extremes. In particular, the dependent variable is assumed to be a mixed random
variable, obtained as the mixture of a Bernoulli and a beta random variables. The endpoints
of zero and one are modelled by a logistic regression model. The values belonging to the interval
(0,1) are assumed to be beta distributed and their mean and dispersion are jointly modelled by
using two link functions. The regression model proposed here accommodates skewness and heteroscedastic
errors. Finally, an application to loan recovery process of Italian banks is also provided.
Keywords: Proportions, Mixed Random Variable, Beta Regression, Skewness, Heteroscedasticity.

The analysis of the passenger satisfaction as a formative second-order construct

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digital
Year:
2012

SUMMARY
The aim of the paper is to define a new concept of global measure for the Passenger Satisfaction
(PS), conceived as second-order latent variables (Henseler and Chin, 2010), and a new estimation
approach to its measurement. This idea arises from theoretical and methodological limits of the existent
models in correctly capturing the construct of satisfaction and the relationships with its subdimensions.
The two main approaches to the estimation of higher-order constructs through the Partial
Least Squares Path Modeling (PLS-PM) are presented: the so called Repeated Indicators and
the Two-Step approaches. Some criticisms of these methodologies are highlighted and a solution to
the issue of the identification of formative second-order constructs is suggested through the adoption
of a Hybrid Two-Step approach for solving the presented PS case study. Three ways of modeling
PS are then compared: a Base Model, where PS is measured as a traditional first-order construct,
and two second-order models estimated, respectively, through the Repeated Indicators and the Hybrid
Two-Step. Results are discussed.
Keywords: Passenger Satisfaction, Second Order Latent Variables, Partial Least Squares Path Modeling,
Hybrid Two-Step Approach.

The confluent hypergeometric-mixture of Polisicchio distributions: a generalized Zenga distribution

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digital
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.

Interpreting clusters and their bipolar means: a case study

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digital
Year:
2013

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

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digital
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.

Application of Zenga’s distribution to a panel survey on household incomes of European Member States

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digital
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.

Minimal sample size for testing trinomial proportions for given precision of probability of type I error

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digital
Year:
2013

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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A Data-Driven Approach to Multivariate Monte Carlo Simulation

Application of Nonparametric Stability Methods in Chickpea (Cicer Arietinum L.) Crop Under Diverse Environments

Application of Nonparametric Stability Methods in Chickpea (Cicer Arietinum L.) Crop Under Diverse Environments

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