幂律、价格模型和帕累托2型分布
Power Laws, the Price Model, and the Pareto type-2 Distribution
摘要：
我们考虑D的一个版本。普赖斯的书目网络增长模型，其中在每次迭代中，恒定数量的引用根据偶然（均匀分布）和优先（富人更富有）规则的加权组合随机分配。而不是依赖于典型的主方程的方法，我们制定和解决这个问题的排名大小分布。我们表明，渐近地，这样的过程导致一个帕累托2型分布与一个有吸引力的可解释的参数化。我们证明了在一个独立的Paretian样本中，用秩-大小分布表示的Price模型的解与顺序统计量的期望值一致。我们研究的偏差和均方误差的基础模型参数的三个表现良好的估计。对大量学术论文的实证分析不仅在分布的尾部（在幂律框架中通常是这种情况），而且在整个领域都有很好的拟合。有趣的是，估计的模型表明更高程度的优先附加引用和更小的随机性比以前的研究。
英文摘要：
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.
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