中等规模利润区的非吉卜拉特对数正态分布
The log-normal distribution from Non-Gibrat's law in the middle scale region of profits
摘要：
利用2003- 2005年日本企业的利润数据，我们在运动学上展示了中等规模区域的静态对数正态分布。在推导中，采用了详细平衡下的非吉卜拉特定律和以下两个近似。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，划分成箱的增长率分布的原点的值是恒定的。在数据库中一致地确认了推导。这一静态过程适用于一个准静态系统。我们动态地描述了一个准静态的对数正态分布中尺度区域。在推导中，采用了详细拟平衡下的非Gibrat定律，并在静态系统中确定了两个近似。结果表明，在大尺度区域，其分布服从变Pareto指数的幂律分布，而在中尺度区域，其分布服从准静态对数正态分布。在分布中，不仅Pareto指数的变化，而且对数正态分布的方差的变化取决于详细拟平衡参数。结果表明，Pareto指数与对数正态分布的方差是相关的。
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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