Frequency analysis is often used to investigate the structure of systems representing multi-scale real-world phenomena. In many different environments, functional relationships characterized by a power law have been recognized, but, in many cases this simple model has turned out to be absolutely inadequate and other models have been proposed. In this paper, we propose a general abstract model which constitutes a unifying framework, including many models found in literature, like the mixed model, the exponential cut-off and the log-normal. It is based on a discrete-time stochastic process, which leads to a recurrence relation describing the temporal evolution of the system. The steady state solution of the system highlights the probability distribution, which underlies the frequency behavior. A particular instance of the general model, called cubic-cut-off, was analyzed and tested in a number of experiments, producing good answers in difficult cases, even in the presence of peculiar behaviors

A Model for the Frequency Distribution of Multi-Scale Phenomena

Ornella Menchi
Co-primo
Membro del Collaboration Group
;
Francesco Romani
Co-primo
Membro del Collaboration Group
2020

Abstract

Frequency analysis is often used to investigate the structure of systems representing multi-scale real-world phenomena. In many different environments, functional relationships characterized by a power law have been recognized, but, in many cases this simple model has turned out to be absolutely inadequate and other models have been proposed. In this paper, we propose a general abstract model which constitutes a unifying framework, including many models found in literature, like the mixed model, the exponential cut-off and the log-normal. It is based on a discrete-time stochastic process, which leads to a recurrence relation describing the temporal evolution of the system. The steady state solution of the system highlights the probability distribution, which underlies the frequency behavior. A particular instance of the general model, called cubic-cut-off, was analyzed and tested in a number of experiments, producing good answers in difficult cases, even in the presence of peculiar behaviors
Favati, Paola; Lotti, Grazia; Menchi, Ornella; Romani, Francesco
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/1076370
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