基于随机排列集最大熵的幂律分布

IF 3.3 3区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Fractals-Complex Geometry Patterns and Scaling in Nature and Society Pub Date : 2023-08-09 DOI:10.1142/s0218348x23500780

Zihan Yu, Z. Li, Yong Deng

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引用次数: 1

摘要

在所有的概率分布中，幂律分布是一个有趣的分布，许多研究者对此进行了研究。然而，幂律分布的推导仍然是一个没有定论的话题。导出分布有多种方法，其中最大熵原理是一种特殊的方法。随机排列集熵作为随机排列集的一种不确定性测度，是一种新提出的具有特殊性的熵。利用RPS的最大熵推导幂律分布是一种很有前途的方法。本文给出了RPS熵的若干约束条件。幂律分布可以用最大熵原理最终导出。数值实验表明了所提出的推导方法的特点。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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POWER LAW DISTRIBUTION BASED ON MAXIMUM ENTROPY OF RANDOM PERMUTATION SET

Among all probability distributions, power law distribution is an intriguing one, which has been studied by many researchers. However, the derivation of power law distribution is still an inconclusive topic. For deriving a distribution, there are various methods, among which maximum entropy principle is a special one. Entropy of random permutation set (RPS), as an uncertainty measure of RPS, is a newly proposed entropy with special features. Deriving power law distribution with maximum entropy of RPS is a promising method. In this paper, certain constraints are given to constrain the entropy of RPS. Power law distribution is able to be finally derived with maximum entropy principle. Numerical experiments are done to show characters of proposed derivation.

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来源期刊

Fractals-Complex Geometry Patterns and Scaling in Nature and Society 数学-数学跨学科应用

CiteScore

7.40

自引率

23.40%

发文量

319

审稿时长

>12 weeks

期刊介绍： The investigation of phenomena involving complex geometry, patterns and scaling has gone through a spectacular development and applications in the past decades. For this relatively short time, geometrical and/or temporal scaling have been shown to represent the common aspects of many processes occurring in an unusually diverse range of fields including physics, mathematics, biology, chemistry, economics, engineering and technology, and human behavior. As a rule, the complex nature of a phenomenon is manifested in the underlying intricate geometry which in most of the cases can be described in terms of objects with non-integer (fractal) dimension. In other cases, the distribution of events in time or various other quantities show specific scaling behavior, thus providing a better understanding of the relevant factors determining the given processes. Using fractal geometry and scaling as a language in the related theoretical, numerical and experimental investigations, it has been possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iterative functions, colloidal aggregation, biological pattern formation, stock markets and inhomogeneous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality. The main challenge of the journal devoted exclusively to the above kinds of phenomena lies in its interdisciplinary nature; it is our commitment to bring together the most recent developments in these fields so that a fruitful interaction of various approaches and scientific views on complex spatial and temporal behaviors in both nature and society could take place.