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Complexity measures for probability distributions with infinite domains

Author

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  • Felipe A. Rizzi

    (Escola Politécnica da Universidade de São Paulo)

  • José Roberto C. Piqueira

    (Escola Politécnica da Universidade de São Paulo)

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. Graphic abstract

Suggested Citation

  • Felipe A. Rizzi & José Roberto C. Piqueira, 2021. "Complexity measures for probability distributions with infinite domains," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(3), pages 1-8, March.
    • Handle: RePEc:spr:eurphb:v:94:y:2021:i:3:d:10.1140_epjb_s10051-021-00064-4
    DOI: 10.1140/epjb/s10051-021-00064-4
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