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digital STATISTICA & APPLICAZIONI - 2012 - 2
Digital issue
issue 2 - 2012
publisher Vita e Pensiero
format Digital issue | Pdf
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The Dagum distribution in reliability analisys
by Mariangela Zenga, Filippo Domma, Giovanni Latorre pages: 17 Download
This work proposes the use of the Dagum model (Dagum, 1977) in the reliability theory. The main motivation is that the hazard rate of this model is very flexible; in fact, it is proved (Domma, 2002) that, according to the values of the parameters, the hazard rate of the Dagum distribution has a decreasing, or an Upside-down Bathtub, or Bathtub and then Upside-down Bathtub failure rate. This work studies some features of the Dagum distribution as the reversed hazard rate, the mean and variance of the random variables residual life and reversed residual life and their monotonicity properties. Two published data sets have been analyzed for illustrative purposes.

Keywords: Burr III distribution, Reversed Hazard Function, Mean Residual Life, Mean Waiting Time, Variance of Residual Life and Reversed Residual Life.
Testing for preference change in marketing or opinion research
by Angiola Pollastri, Daniele Riva pages: 16 Download
Let us suppose we have two important products or parties or opinions indicated respectively by A and B and a pool of small other choices indicated by C and we are interested in understanding if the percentage of preferences for A and the percentage of preferences for B are unchanged, increased or decreased after some event (f.i. advertising). If the sample size is big, we propose to use a two stage hypotheses test proposed by Duncan (Miller, 1981) and improved by Pollastri (2008). The test considered is based on the exact distribution of the absolute maximum (Zenga, 1979) and on the exact distribution of the absolute minimum (Pollastri and Tornaghi, 2004) of the components of a Bivariate Correlated Normal. Tables of the critical values are reported. The test proposed allows to accept one of the nine hypotheses about the invariance or increasing or decreasing of the percentage of A combined with the three movements of the percentage of B.

Keywords: Trinomial Distribution, Bivariate Correlated Normal, Two Stage Hypotheses Test, Absolute Maximum and Minimum.
First applications of a new three-parameter distribution for non-negative variables
by Michele Zenga, Leo Pasquazzi, Mariangela Zenga pages: 17 Download
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.
Estimation of the variance for logistic distribution under ranked set sampling and simple random sampling: a comparative study
by Walid Ahmad Abu-Dayyeh, Sameer A. Al-Subh pages: 9 Download
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
by Raffaella Calabrese pages: 13 Download
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
by Enrico Ciavolino, Mariangela Nitti pages: 14 Download
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.