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Elsevier, Physica A: Statistical Mechanics and its Applications, (444), p. 271-275, 2016

DOI: 10.1016/j.physa.2015.10.040

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A comparison of LMC and SDL complexity measures on binomial distributions

Journal article published in 2015 by José Roberto C. Piqueira ORCID
This paper is available in a repository.
This paper is available in a repository.

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Abstract

The concept of complexity has been widely discussed in the last forty years, with a lot of thinking contributions coming from all areas of the human knowledge, including Philosophy, Linguistics, History, Biology, Physics, Chemistry and many others, with mathematicians trying to give a rigorous view of it. In this sense, thermodynamics meets information theory and, by using the entropy definition, López-Ruiz, Mancini and Calbet proposed a definition for complexity that is referred as LMC measure. Shiner, Davison and Landsberg, by slightly changing the LMC definition, proposed the SDL measure and the both, LMC and SDL, are satisfactory to measure complexity for a lot of problems. Here, SDL and LMC measures are applied to the case of a binomial probability distribution, trying to clarify how the length of the data set implies complexity and how the success probability of the repeated trials determines how complex the whole set is.