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摘要翻译：
本文对巴西个人收入分配的演变进行了实证研究。研究了1978年至2005年的年度样本，发现99%的经济条件较差的人口的个人收入的互补累积分布很好地表现为G(x)=\exp[\exp(A-Bx)]$的Gompertz曲线，其中$x$是归一化的个人收入。人口中剩余1%最富有部分的互补累积分布由Pareto幂律分布$P(x)=\betax^{-\alpha}$很好地表示。这一结果意味着，与其他国家一样，巴西的收入分配也是以明确界定的两级制度为特征的。参数$a$，$b$，$\alpha$，$\beta$是通过混合边界条件，归一化和拟合方法确定的。由于Gompertz曲线是增长模型的特征，它在这里的出现表明，收入分配的这些模式可能是潜在经济系统增长动态的结果。此外，我们还发现Gompertzian和Paretian两个分量相对于总收入的百分比份额呈现出一个周期约为4年的近似循环模式，每个分量的最大峰值和最小峰值约每2年交替一次。这一发现表明，巴西经济系统的增长动力可能遵循古德温型类模型动力，其基础是对经济增长和周期的Lotka-Volterra方程的应用。
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英文标题：
《Evidence for the Gompertz Curve in the Income Distribution of Brazil
1978-2005》
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作者：
Newton J. Moura Jr. (1), Marcelo B. Ribeiro (2) ((1) IBGE - Brazilian
Institute for Geography and Statistics, Geosciences Directorate, Rio de
Janeiro, (2) Physics Institute, University of Brazil - UFRJ, Rio de Janeiro)
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最新提交年份：
2008
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：General Finance 一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics 物理学
二级分类：Adaptation and Self-Organizing Systems 自适应和自组织系统
分类描述：Adaptation, self-organizing systems, statistical physics, fluctuating systems, stochastic processes, interacting particle systems, machine learning
自适应，自组织系统，统计物理，波动系统，随机过程，相互作用粒子系统，机器学习
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一级分类：Physics 物理学
二级分类：Physics and Society 物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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英文摘要：
This work presents an empirical study of the evolution of the personal income distribution in Brazil. Yearly samples available from 1978 to 2005 were studied and evidence was found that the complementary cumulative distribution of personal income for 99% of the economically less favorable population is well represented by a Gompertz curve of the form $G(x)=\exp [\exp (A-Bx)]$, where $x$ is the normalized individual income. The complementary cumulative distribution of the remaining 1% richest part of the population is well represented by a Pareto power law distribution $P(x)= \beta x^{-\alpha}$. This result means that similarly to other countries, Brazil's income distribution is characterized by a well defined two class system. The parameters $A$, $B$, $\alpha$, $\beta$ were determined by a mixture of boundary conditions, normalization and fitting methods for every year in the time span of this study. Since the Gompertz curve is characteristic of growth models, its presence here suggests that these patterns in income distribution could be a consequence of the growth dynamics of the underlying economic system. In addition, we found out that the percentage share of both the Gompertzian and Paretian components relative to the total income shows an approximate cycling pattern with periods of about 4 years and whose maximum and minimum peaks in each component alternate at about every 2 years. This finding suggests that the growth dynamics of Brazil's economic system might possibly follow a Goodwin-type class model dynamics based on the application of the Lotka-Volterra equation to economic growth and cycle.
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PDF链接：
https://arxiv.org/pdf/0812.2664
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