A generalized preferential attachment model for business firms growth rates II. Mathematical treatment
A generalized preferential attachment model for business firms growth rates II. Mathematical treatment
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DOI：
10.1140/epjb/e2007-00165-8
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发表时间：
2007-05-01
影响因子：
1.6
通讯作者：
Stanley, H. E.
中科院分区：
文献类型：
--
作者：
Buldyrev, S. V.;Pammolli, F.;Stanley, H. E.
我们提出了一个优先依恋增长模型，以获得类别中单位数量K的分布P(K)，这些类别可能代表企业或其他社会经济实体。我们发现P(K)在其中心部分由指数为phi = 2+b/(1-b)的幂律描述，该幂律取决于新类别b进入的概率。在城市人口的特定问题中，该分布相当于众所周知的Zipf定律。在没有新类进入的情况下，分布P(K)是指数型的。利用P(K)的解析形式，并假设单位按比例增长，我们推导出企业增长率的分布P(g)。该模型预测P(g)在中心部分有一个拉普拉斯顶点和指数为zeta = 3的渐近幂律尾部。我们通过模拟来测试使用启发式论证导出的解析表达式。该模型还可以解释企业增长率的规模-方差关系。
We present a preferential attachment growth model to obtain the distribution P(K) of number of units K in the classes which may represent business firms or other socio-economic entities. We found that P(K) is described in its central part by a power law with an exponent phi = 2+b/(1-b) which depends on the probability of entry of new classes, b. In a particular problem of city population this distribution is equivalent to the well known Zipf law. In the absence of the new classes entry, the distribution P(K) is exponential. Using analytical form of P(K) and assuming proportional growth for units, we derive P(g), the distribution of business firm growth rates. The model predicts that P(g) has a Laplacian cusp in the central part and asymptotic power-law tails with an exponent zeta = 3. We test the analytical expressions derived using heuristic arguments by simulations. The model might also explain the size-variance relationship of the firm growth rates.