Pier Luigi Novi Inverardi

Stieltjes moment problem via fractional moments

Stieltjes moment problem is considered to recover a probability density function from the knowledge of its infinite sequence of ordinary moments. The approximate density is obtained through maximum entropy technique, under the constraint of few fractional moments. The latter are numerically obtained from the infinite sequence of ordinary moments and are chosen in such a way as to convey the maximum information content carried by the ordinary moments. As a consequence a model with few parameters is obtained and intrinsic numerical instability is avoided. It is proved that the approximate density is useful for calculating expected values and some other interesting probabilistic quantities.

Hausdorff moment problem via fractional moments

We outline an efficient method for the reconstruction of a probability density function from the knowledge of its infinite sequence of ordinary moments. The approximate density is obtained resorting to maximum entropy technique, under the constraint of some fractional moments. The latter ones are obtained explicitly in terms of the infinite sequence of given ordinary moments. It is proved that the approximate density converges in entropy to underlying density, so that it turns out to be useful for calculating expected values.

Maxentropic solution of fractional moment problems

The problem of reconstructing a function from the knowledge of a few of its moments is a special case of the problem inverting an integral transform when there are finitely many data points. The classical method of maximum entropy and the method of maximum entropy in the mean are well suited to attack these problems. What is interesting is that when we are free to choose the data points, the choice can be made to improve the quality of the reconstruction when the method of maximum entropy is used too. In this note we review how to apply these methods and compare them in a couple of examples.

Moment information and entropy evaluation for probability densities

Abstract How much information does the sequence of integer moments carry about the corresponding unknown absolutely continuous distribution? We prove that a reliable evaluation of the corresponding Shannon entropy can be done by exploiting some known theoretical results on the entropy convergence, uniquely involving exact moments without solving the underlying moment problem. All the procedure essentially rests on the solution of linear systems, with nearly singular matrices, and hence it requires both calculations in high precision and a pre-conditioning technique. Numerical examples are provided to support the theoretical results.

Choosing the rightweight model for web site quality evaluation

One of the most critical decisions in a quality evaluation project is to establish the level at which to analyse the characteristics of the Web sites. This choice should be driven by the underlying goals of the evaluation. Scalability and flexibility are thus desiderable features of the models used to evaluate the quality of a Web site. In this paper we describe two separate studies of Regional Tourist Boards in the Alps that were conducted using the meta-model 2QCV3Q. Specifically, we will show that the results of the first study - based on a lightweight model - are consistent with those obtained with the more detailed heavyweight model in the second study.

Awareness and Exploitation of the Potential of the Web by SMTEs: The Case of Alpine Hotels in Italy and France

The economic literature has clearly shown the potential of the introduction of the ICTs in the management of the firms, starting from the seminal research of the MIT in the Ninetines. The question is if small tourist businesses have used correctly and widely the new technologies, gaining competitive advantages and improving their market results. The paper presents the results of a field research on this topic, managed by the eTourism Research Group in the territory of the Alps, where the tourist offering is based on small — or micro — businesses. The analysis allows to identify both positive and negative results, highlighting some lacks in the use of the Web by the SMTEs and suggesting some areas of improvement.

The Web as (a Weak) Enabler of New Marketing Approaches. An In-Depth Study of SMTEs in the Dolomites

This paper analyses the impact of ICTs on the strategic and organisational behaviour of hotel enterprises in the Dolomites, one of the main tourist areas in the Alps. The results are from two research projects conducted in 2005 and which involved 1) in-depth personal interviews of a sampling of 43 hotelkeepers and 2) the evaluation of the Web sites of 147 hotels. The effects of the widespread application of new ICTs among small hotels arc also discussed, looking specifically at whether and to what degree such technologies have supported the creation of a network among SMTEs and enabled innovative processes in marketing. From the two research projects it is possible to conclude that as yet the Web has not been an enabler of processes for structural, managerial or commercial reorganisation for SMTEs in the Dolomites. Hotelkeepers had a positive perception of the usefulness of new ICTs tools such as email and Web sites and also that they arc a wise economic investment. Nonetheless, these technologies have been used only to conduct traditional business in a new way, bringing advantages in terms of efficiency and efficacy, but not being used to redesign the internal management and organisational structure, nor the network of relations with local partners within the value chain. New ICTs have had a typical veiling effect insomuch as they have been used for traditional tasks but lack the capability to have a definitive effect on the reorganisation of management processes. A possible solution to achieve this result for SMTEs is to adopt a business culture with a broader strategic vision that is more open to collaboration. Unless such a new approach is taken the possibility of using Internet to redefine the business model at an individual and destination level would probably be lost.

Fractional Moments and Maximum Entropy: Geometric Meaning

We consider the problem of recovering a probability density on a bounded or unbounded subset D of [0, ∞), from the knowledge of its sequence of fractional moments within a maximum entropy (MaxEnt) setup. Based upon entropy convergence results previously formulated, the fractional moments are selected so that the entropy of the MaxEnt approximation be minimum. A geometric interpretation of the reconstruction procedure is formulated as follows: the two moment curves generated by the unknown density and its MaxEnt approximation are interpolating in Hermite-Birkoff sense; that is, they are both interpolating and tangent at the selected nodes.

The role of the regional tourist boards in the destination marketing policies. The case of the dolomites

In recent years the scientific community has focused on the study of tourist destinations from a strategic-managerial perspective. Questions remain, however, regarding who can manage the destination as a system and facilitate coordination among local operators. In the light of a research conducted in the Dolomites (an Italian alpine region) this paper seeks to define some possible strategies for destination marketing by Regional Tourist Boards (RTBs) with a view to identifying the characteristics associated with an integrated tourist destination.ResumenA lo largo de los últimos aúos la comunidad cientúfica ha centrado sus esfuerzos en el estudio de los destinos turísticos desde una perspectiva estratígico-gerencial. Quedan, sin embargo, cuestiones por resolver en relatión con quión puede gestionar un destino en tanto en cuanto que sistema y facilitar la coordinatión de los operadores locales. Tratando de aportar alguna luz en este sentido a partir de una investigatión llevada a cabo en la región alpina italiana de los Dolomitas, el propósito del presente trabajo consiste en determinar algunas estrategias de marketing susceptibles de aplicación por las Corporaciones de Turismo Regionales, tratando de identificar las características asociadas a un destino turístico integrado.

Entropy and density approximation from Laplace transforms

How much information does the Laplace transforms on the real line carry about an unknown, absolutely continuous distribution? If we measure that information by the Boltzmann-Gibbs-Shannon entropy, the original question becomes: How to determine the information in a probability density from the given values of its Laplace transform. We prove that a reliable evaluation both of the entropy and density can be done by exploiting some theoretical results about entropy convergence, that involve only finitely many real values of the Laplace transform, without having to invert the Laplace transform.We provide a bound for the approximation error of in terms of the Kullback-Leibler distance and a method for calculating the density to arbitrary accuracy.