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Complexity measures for probability distributions with infinite domains

  • Regular Article - Statistical and Nonlinear Physics
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Abstract

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.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Data sharing not applicable to this article as no datasets were generated or analysed during the current study.]

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Acknowledgements

JRCP was supported by the Brazilian Research Council (CNPq), Grant number 302883/2018-5.

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Authors and Affiliations

  1. Escola Politécnica da Universidade de São Paulo, Av. Prof. Luciano Gualberto, tv. 3-158, São Paulo, SP, Brazil

    Felipe A. Rizzi & José Roberto C. Piqueira

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  1. Felipe A. Rizzi
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  2. José Roberto C. Piqueira
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Correspondence to José Roberto C. Piqueira.

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Rizzi, F.A., Piqueira, J.R.C. Complexity measures for probability distributions with infinite domains. Eur. Phys. J. B 94, 62 (2021). https://doi.org/10.1140/epjb/s10051-021-00064-4

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