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A model for the frequency distribution of multi-scale phenomena

The 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, is analyzed and tested in a number of experiments producing good answers in difficult cases even in presence of peculiar behaviors


2020

Autori esterni: G. Lotti (Dipart. di Matematica, University of Parma, Parma, Italy), O. Menchi (Dipart. di Informatica, University of Pisa, Pisa, Italy), F. Romani (Dipart. di Informatica, University of Pisa, Pisa, Italy)
Autori IIT:

Tipo: Rapporto Tecnico
Area di disciplina: Mathematics
IIT TR-19/2020

File: IIT-19-2020.pdf

Attività: Algoritmica per tecnologie web