摘要翻译：
利用日本企业2003-2005年的利润数据，在运动学上呈现出中等规模区域的静态对数正态分布。在推导过程中，采用了详细平衡条件下的非直布罗特定律和以下两种近似。首先将利润增长率的概率密度函数描述为帐篷型指数函数。其次，分箱增长率分布的原点值是不变的。该推导在数据库中得到一致的确认。将此静态过程应用于准静态系统。我们在中尺度区域动态地描述了一个准静态对数正态分布。在推导中，采用了详细拟平衡下的一个非直布罗特定律，并在静态系统中确认了两个近似。结果表明，在大尺度区域内，合成分布为Pareto指数变化的幂律分布，而在中尺度区域内，合成分布为准静态对数正态分布。在分布中，Pareto指数的变化以及对数正态分布方差的变化都依赖于详细拟平衡的参数。结果表明，Pareto指数和对数正态分布的方差是相互联系的。
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英文标题：
《The log-normal distribution from Non-Gibrat's law in the middle scale
  region of profits》
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作者：
Atushi Ishikawa
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最新提交年份：
2007
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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：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：
  Employing profits data of Japanese firms in 2003--2005, we kinematically exhibit the static log-normal distribution in the middle scale region. In the derivation, a Non-Gibrat's law under the detailed balance is adopted together with following two approximations. Firstly, the probability density function of profits growth rate is described as a tent-shaped exponential function. Secondly, the value of the origin of the growth rate distribution divided into bins is constant. The derivation is confirmed in the database consistently.   This static procedure is applied to a quasi-static system. We dynamically describe a quasi-static log-normal distribution in the middle scale region. In the derivation, a Non-Gibrat's law under the detailed quasi-balance is adopted together with two approximations confirmed in the static system. The resultant distribution is power-law with varying Pareto index in the large scale region and the quasi-static log-normal distribution in the middle scale region. In the distribution, not only the change of Pareto index but also the change of the variance of the log-normal distribution depends on the parameter of the detailed quasi-balance. As a result, Pareto index and the variance of the log-normal distribution are related to each other.
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PDF链接：
https://arxiv.org/pdf/0705.1056