Modelling income distributions using Tsallis statistics

IF 3.1 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
Stefan Hutzler, John A. Joseph, Samuel Marks, Peter Richmond
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引用次数: 0

Abstract

The World Bank provides data sets for income distributions of over 140 countries. We demonstrate that the large majority of these can be described by a distribution derived from Tsallis statistics, which is a generalisation of Boltzmann statistics, applicable to non-equilibrium systems. (For nine countries the log-normal distribution is statistically preferred.) The result of our least square fits of the income distributions suggests a roughly linear variation of the two Tsallis fit parameters, λ (an inverse temperature), and the index of non-extensivity, q, for q1.5 (with q=1 corresponding to Boltzmann statistics). Values of the Gini index (a measure of inequality) for the different countries, obtained from our least square fits, are in good agreement with published World Bank data. Finally, we present an expression for the cumulative distribution for income data which is normalised with respect to the average income, to allow for an estimation of the power law exponent describing its tail.
使用Tsallis统计建模收入分配
世界银行提供了140多个国家的收入分配数据集。我们证明了这些中的绝大多数可以用来自Tsallis统计量的分布来描述,Tsallis统计量是Boltzmann统计量的推广,适用于非平衡系统。(有9个国家在统计上更倾向于对数正态分布。)我们对收入分布的最小二乘拟合结果表明,两个Tsallis拟合参数λ(逆温度)和非扩散性指数q在q≤1.5时大致呈线性变化(其中q=1对应Boltzmann统计量)。根据我们的最小二乘拟合得出的不同国家的基尼系数(衡量不平等程度的指标)值与世界银行公布的数据非常吻合。最后,我们提出了收入数据累积分布的表达式,该表达式相对于平均收入进行了归一化,以便对描述其尾部的幂律指数进行估计。
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来源期刊
CiteScore
7.20
自引率
9.10%
发文量
852
审稿时长
6.6 months
期刊介绍: Physica A: Statistical Mechanics and its Applications Recognized by the European Physical Society Physica A publishes research in the field of statistical mechanics and its applications. Statistical mechanics sets out to explain the behaviour of macroscopic systems by studying the statistical properties of their microscopic constituents. Applications of the techniques of statistical mechanics are widespread, and include: applications to physical systems such as solids, liquids and gases; applications to chemical and biological systems (colloids, interfaces, complex fluids, polymers and biopolymers, cell physics); and other interdisciplinary applications to for instance biological, economical and sociological systems.
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