STATISTICA & APPLICAZIONI - 2011 - 1

SUMMARY
Recently Zenga (2010) has proposed a new three-parameter density function f (x : µ; α; θ), (µ > 0; α > 0; θ > 0), for non-negative variables. The parameter µ is equal to the expectation of the distribution. The new density has positive asymmetry and Paretian right tail. For θ > 1, Zenga (2010) has obtained the expressions of: the distribution function, the moments, the truncated moments, the mean deviation and Zenga’s (2007a) point inequality A(x) at x = µ. In the present paper, as to the general case θ > 0, the expressions of: the distribution function, the ordinary and truncated moments, the mean deviations and Zenga’s point inequality A (µ) are obtained. These expressions are more complex than those previously obtained for θ > 1 by Zenga (2010). The paper is enriched with many graphs of: the density functions (0.5 ≤ θ ≤ 1.5), the Lorenz L(p) and Zenga’s I (p) curves as well as the hazard and survival functions.
Keywords: Non-Negative Variables, Positive Asymmetry, Paretian Right Tail, Beta Function, Lorenz Curve, Zenga’s Inequality Curve, Hazard Function, Survival Function.

SUMMARY
The purpose of this article is to study the ploynomial linear regression model under the median ranked set sampling (MRSS) scheme introduced by Muttlak (1997). If the response variable can be more easily ranked than quantified, then we use the MRSS to collect data by ranking on the response variable. We obtain estimators and confidence intervals for the polynomial regression parameters under MRSS when the errors have a symmetric distribution. We also show that the least square estimators, under MRSS, are more efficient than their SRS counterparts and give illustrating examples.
Keywords: Median Ranked Set Sample, Polynomial Regression.

SUMMARY
The aim of an important branch of inequality analysis is the investigation into the features of the distribution models with specific kinds of inequality curves. This paper is an investigation into the distribution model with linear inequality I ðpÞ curve. The definition of the corresponding distribution function, and a procedure to obtain the probability density function are described. An analysis of the constraints that the parameters of the line must satisfy is also provided. The methodological results are supported by two applications with real air traffic control data.
Keywords: Inequality, Lorenz L(p) Curve, Zenga I (p) Curve, Income Distributions.

SUMMARY
The nonparametric Kolmogorov-Smirnov goodness of fit test is employed to test if a random sample comes from a specified continuous distribution function. When this hypothesis is not satisfied the test is no longer applicable accurately. In the last years relatively little attention has been paid to the problems of the application of Kolmogorov-Smirnov test for discrete distributions. In this paper we present a survey of the previous works, we propose a procedure to apply the test to discrete random variables and we define the corresponding statistic. Moreover for some given distributions the exact critical values are tabulated and a comparison with the continuous case is made.
Keywords: Goodness of Fit Test, Discrete Distributions, Empirical Distribution Function.

SUMMARY
Nowadays, in Italy, surveys carried out to measure Customer Satisfaction in Public Services are going to become more important and systematic. The new directive form Public Function Office (2004) emphasizes the fundamental role of users’ opinions to drive and possibly improve public services. The administrators have to consider users’ opinions, because these judgments are useful to offer more acceptable and appreciable services. Measure Customer Satisfaction in Public services is not a simple task and for this reason it is at the center of growing attentions. In this paper, after dealing some theoretical aspects related to this matter, the case of an Italian Chamber of Commerce is considered and different statistical methods to analyze users’ satisfaction data are proposed.
Keywords: Service Quality, Heterogeneity and Dissimilarity Index, Rasch Analysis, Overall Satisfaction.

SUMMARY
Mangrove forests’ contribution to the coastal biodiversity is invaluable. They serve as habitat for marine flora and fauna and also cleanse the water. They act as breeding ground to many fish species. Still the mangroves are destroyed large scale for aquaculture farming and also for tourism industry. We have conducted a contingent valuation survey to study the willingness of coastal fishermen community in Uttara Kannada district of Karnataka, India to contribute towards the cultivation of mangroves. Zero Inflated Poisson model was used to estimate the number of days fishermen willing to work. We have also identified the factors influencing their decision to participate or not to participate in the program.
Keywords: Contingent Valuation, Willingness to Work, Zero Inflated Poisson Distribution, Model Based Estimator.