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digital STATISTICA & APPLICAZIONI - 2008 - 1
Digital issue
issue 1 - 2008
publisher Vita e Pensiero
format Digital issue | Pdf
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A real data validation of some gambling strategies and gambler’s expectations in the roulette game
by Antonio Gambini, Enrico Di Bella pages: 13 Download
The game of the roulette has stimulated the creation of gambling strategies more than any other casino game. The goal stated by many of these strategies is the overturning of the unfavourable condition of the gambler guaranteeing a positive average return. Although well known in literature that this result cannot be obtained, the decision of how and how much the player can bet allows the maximization of the probability of some specific goal prearranged by the gambler. In this work some of the most famous systems applied in casinos are analyzed and confronted. The availability of the come ups of the numbers of a single roulette in the course of a solar year of a famous Italian public casino, allows the verification of the unbiasedness of the wheel and the faithful adhesion of the empirical come ups to those regarding the correspondent discrete uniform theoretical model.
Risk aversion and propensity to risk of complex groups: an empirical analysis for the board of the foundation for the saving bank of Florence
by Francesco Chelli, Alberto Niccoli pages: 16 Download
The paper deals with the estimation of the attitude to risk of a group of people, the Board of the Foundation for the Saving Bank of Florence. A specific method is used: the so-called trade-off method, both with the outward and the inward procedure. In a previous study Bacci and Chiandotto (2002) presented the data, holding that the risk attitude for the Board implies propensity to risk when low levels of income and utility are concerned, and risk aversion for higher values of income/utility. Different theoretical utility functions are estimated in this paper: very simple ones, like the power utility function, and more complex ones, including the specification used in Bacci and Chiandotto (2003). Our results imply either risk neutrality (aversion), when so-called outward trade-off procedure (inward trade-off procedure) data alone are used or, perhaps, risk aversion (propensity) when low (high) values for income/utility are considered.
Synthesis of statistical indicators to evaluate quality of life in the Italian province
by Roberto Gismondi, Massimo Alfonso Russo pages: 24 Download
This work remarks the need to carefully evaluate the real importance of each variable used in a multivariate analysis context, with particular regard to cases when an overall performance ranking is the main final purpose. In particular, both a preliminary transformation of variables – aimed at reducing asymmetry and variability of their variation ranges – and the evaluation of their intrinsic explicative power – through redundancy analysis and weighting methods – are proposed. Theoretical and empirical considerations are developed in the frame of quality of life evaluation, carried out at the Italian provinces level on the basis of a yearly survey managed by the Italian economic newspaper ‘‘Il Sole24ore’’. A particular emphasis is given to some normalisation criteria and the case when original variables are grouped ‘‘a priori’’ into logical blocks. A final comparison between the actual ranking method and a series of alternatives is proposed as well.
A note on the bipolar mean: is it a single mean?
by Alessandro Zini pages: 7 Download
In this note a generalisation of the bipolar mean, recently introduced in the literature by Maffenini and Zenga (2005), is presented and discussed. It seems interesting in those contexts, where the categories of an ordinal variable are to be thought as ‘‘non equidistant’’, like in some problems in the customer satisfaction analyses. It is pointed out that the particular bipolar mean chosen for a problem can modify the ‘‘ordering’’ among the frequency distributions with fixed sum N.
Analytical solution for both orthogonal procrustes rotation problems with determinant constraints
by Sebastián Torcida, Nélida Winzer pages: 9 Download
Since first formulated, orthogonal Procrustes analysis has been mainly related to the biometrical study of shapes (shape analysis) based on landmarks. Essentially, this is a method to superimpose two configurations of points by means of a similarity – a combination of a translation term, an isotropic change of scale and an orthogonal transformation – in order to produce an optimal fit, in a least-squares sense. And among them, the problem of finding the best orthogonal transformation has its own particular interest from a biological point of view and it is known as the Procrustes rotation (PR) problem. In morphometrics, the presence of a particular type of symmetry often constrains the search of the PR to be either a determinant 1 or a determinant -1 orthogonal matrix. While the analytical solution to the first problem is well known, a formal proof of the solution to the latter is still required. A common-analytical proof of the solution for both constrained PR problems is given in this work, based on the standard (and unique) singular-value descomposition.
The regression estimator in presence of ‘‘not at home’’
by Walter Maffenini pages: 15 Download
Being temporarily not at home can often cause the impossibility to give out a questionnaire to each selected unit of a sample; moreover, a high percentage of nonrespondents can strongly affect the quality of estimates. In order to solve this problem the ‘‘not at home’’ are usually called back until they become available; however, this methodology highly increases the costs of a survey. The main idea of this paper traces back to an estimation method early proposed by Politz and Simmons; in particular, a new estimator, based on the regression method, is proposed, so that the auxiliary information about the number of evenings spent at home by the units of the target population can be used. The proposed estimator is shown to be unbiased and more efficient than the one based only on the responses of the units being at home when first contacted. Moreover, unlike from the Politz-Simmons estimator, the variance of the proposed estimator can be easily determined and computed. Finally, in order to discuss the asymptotic properties of the regression estimator, the results of some simulations are reported; both the proposed estimator and the Politz-Simmons one turn out to be asymptotically unbiased; however, the regression estimator still proves to be more efficient.