自然与社会环境中的幂律现象和双帕累托对数正态分布

Power law behaviors in natural and social phenomena and the double Pareto lognormal distribution

幂律是在许多自然和社会环境中都能观察到的现象。但如何精确地描述这种现象并合理地解释这种现象的成因却一直令人困扰。双帕累托对数正态分布从随机过程的角度对这一问题给出了一个新的思路。本文首先描述双帕累托对数正态分布的数学推导与生成模型,然后解释此分布为什么会在社交网朋友的数量、互联网文件的大小、股票市场的回报、社会财富的占有、城市人口的规模、油田的储量及森林火灾焚烧的面积等现象中出现的可能原因。

Power law behaviors are ubiquitous in natural and social phenomena.How to accurately describe such behaviors and provide reasonable explanations of why such behaviors occur,however,has long been a standing open problem.The double Pareto lognormal distribution offers,from the stochastic process point of view,a viable approach to this problem.This article elaborates the mathematical concept of the double Pareto lognormal distribution and provides an overview of natural and social phenomena that exhibit such distribution.These include the number of friends in social networks,Internet file sizes,stock market returns,wealth possessions in human societies,human settlement sizes,oil field reserves,and areas burnt from forest wildfire.