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

中文翻译：

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具有无限域的概率分布的复杂性度量

摘要

自上世纪下半叶以来，人们一直在研究复杂性的概念，以发现和联系来自不同学科的思想。根据扩展到生物学和人文科学领域的计算方法，已经提出了几种量化方法，例如洛佩兹·鲁伊斯（López-Ruiz），曼奇尼（Mancini）和卡尔贝特（Calbet）（LMC）；以及Shiner，Davison和Landsberg（SDL）复杂性度量，这些度量以信息熵的概念为定义的核心。但是，这些定义仅限于具有有限域的离散概率分布，从而限制了要研究的系统。这些措施的扩展被提议用于连续概率分布，但是没有讨论具有无限域的离散分布。在这里，我们研究了这些情况，并分析了几种分布，

图形摘要