用福克-普朗克方程模拟欧盟的收入分配
Modeling of income distribution in the European Union with the Fokker-Planck equation
摘要：
在这里，我们应用统计物理学来研究三个（低收入，中等收入和高收入）社会阶层的收入，而不是迄今为止研究的两个（低收入和中等收入）阶层。在阈值非线性Langevin动力学和阈值Fokker-Planck动力学的框架下，我们推导出了一个描述社会各阶层收入的统一公式，并以欧盟2006年和2008年的收入为例。因此，该公式比众所周知的Yakovenko等人的公式更一般。也就是说，我们的公式不仅很好地描述了两个区域，而且同时描述了互补累积分布函数与家庭年收入图中的第三个区域。此外，我们的公式很好地描述了关于这种收入的已知的程式化事实。也就是说，正如预期的那样，该公式为低收入社会阶层提供了Boltzmann-Gibbs收入分布函数，为中等收入社会阶层提供了弱帕累托定律。重要的是，它为高收入社会阶层预测了齐普夫定律（令人满意的近似值）。此外，由于高收入阶层的底层明显降低，中等收入阶层的区域明显缩小。事实上，这种减少使中等收入社会阶层成为中等收入社会阶层。
英文摘要：
Herein, we applied statistical physics to study incomes of three (low-, medium- and high-income) society classes instead of the two (low- and medium-income)classes studied so far. In the frame of the threshold nonlinear Langevin dynamics and its threshold Fokker-Planck counterpart, we derived a unified formula for description of income of all society classes, by way of example, of those of the European Union in year 2006 and 2008. Hence, the formula is more general than the well known that of Yakovenko et al. That is, our formula well describes not only two regions but simultaneously the third region in the plot of the complementary cumulative distribution function vs. an annual household income. Furthermore, the known stylised facts concerning this income are well described by our formula. Namely, the formula provides the Boltzmann-Gibbs income distribution function for the low-income society class and the weak Pareto law for the medium-income society class, as expected. Importantly, it predicts (to satisfactory approximation) the Zipf law for the high-income society class. Moreover, the region of medium-income society class is now distinctly reduced because the bottom of high-income society class is distinctly lowered. This reduction made, in fact, the medium-income society class an intermediate-income society class.
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