论文标题
电力定律，价格模型和帕累托2型分布
Power Laws, the Price Model, and the Pareto type-2 Distribution
论文作者
论文摘要
我们考虑了D. Price模型的书目网络的增长版本，在每个迭代中，根据意外（均匀分布）和优先（Rich-Get-get-Richer）规则的加权组合随机分配恒定的引用。我们不依赖典型的主方程方法，而是根据等级大小的分布来提出和解决此问题。我们表明，这种过程渐近地导致帕累托型2分布具有可解释的参数化。我们证明，按等级尺寸分布表示的价格模型的解决方案与独立的paretian样本中订单统计的预期值一致。我们研究了基础模型参数的三个良好行为估计量的偏差和平方误差。对大型学术论文存储库的经验分析不仅可以在分布的尾部（通常在类似于Power Law的框架中），而且在整个领域都具有良好的契合度。有趣的是，估计的模型表明，比以前的研究比以前的研究更高的优先附加引用和更小的随机性份额。
We consider a version of D. Price's model for the growth of a bibliographic network, where in each iteration a constant number of citations is randomly allocated according to a weighted combination of accidental (uniformly distributed) and preferential (rich-get-richer) rules. Instead of relying on the typical master equation approach, we formulate and solve this problem in terms of the rank-size distribution. We show that, asymptotically, such a process leads to a Pareto-type 2 distribution with an appealingly interpretable parametrisation. We prove that the solution to the Price model expressed in terms of the rank-size distribution coincides with the expected values of order statistics in an independent Paretian sample. We study the bias and the mean squared error of three well-behaving estimators of the underlying model parameters. An empirical analysis of a large repository of academic papers yields a good fit not only in the tail of the distribution (as it is usually the case in the power law-like framework), but also across the whole domain. Interestingly, the estimated models indicate higher degree of preferentially attached citations and smaller share of randomness than previous studies.
