Vita e Pensiero

SUMMARY 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.

SUMMARY 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.

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.

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.

SUMMARY In the ranked set sampling with set size equal to m, there are mm different possible sampling schemes. The aim of this paper is to characterize the optimal sampling scheme via the Fisher information numbers for normal distribution with known coefficient of variation. Moreover, we use the optimal sampling schemes to obtain unbiased estimators for the mean. Also we compare the estimators to their counterparts under the McIntyre’s ranked set sampling scheme. We show that the MLE under optimal sampling scheme is asymptotically more efficient than its counterpart under McIntyre’s RSS. Keywords: Ranked Set Sampling, Fisher Information, Maximum Likelihood, Normal Distribution, Coefficient of Variation.

SUMMARY In the present communication, we discuss some properties of the new Zenga measure I (p) for inequality. Unlike the Lorenz curve, the I (p) curve can be decreasing, increasing and non-monotonic. Various conditions for monotonicity of I (p) are presented. Further some results on a stochastic order based on I (p) are also established. Keywords: Zenga Curve, Lorenz Curve, Stochastic Order, Quantiles.