https://doi.org/10.1140/epjb/s10051-021-00064-4
Regular Article - Statistical and Nonlinear Physics
Complexity measures for probability distributions with infinite domains
Escola Politécnica da Universidade de São Paulo, Av. Prof. Luciano Gualberto, tv. 3-158, São Paulo, SP, Brazil
Received:
16
September
2020
Accepted:
12
February
2021
Published online:
18
March
2021
Since the second half of the last century, the concept of complexity has been studied to find and connect ideas from different disciplines. Several quantifying methods have been proposed, based on computational measures extended to the context of biological and human sciences, as, for instance, the López-Ruiz, Mancini, and Calbet (LMC); and Shiner, Davison, and Landsberg (SDL) complexity measures, which take the concept of information entropy as the core of the definitions. However, these definitions are restricted to discrete probability distributions with finite domains, limiting the systems to be studied. Extensions of these measures were proposed for continuous probability distributions, but discrete distributions with infinite domains were not discussed. Here, these cases are studied and several distributions are analyzed, including the Zipf distribution, considered the paradigmatic model for self-organizing criticality.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2021
