Fitting and goodness-of-fit test of non-truncated and truncated power-law distributions
Fitting and goodness-of-fit test of non-truncated and truncated power-law distributions
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DOI：
10.2478/s11600-013-0154-9
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发表时间：
2013-12-01
期刊：
影响因子：
2.3
通讯作者：
Corral, Alvaro
中科院分区：
文献类型：
--
作者：
Deluca, Anna;Corral, Alvaro
最近，Clauset， Shalizi和Newman提出了一种系统的方法来找出某个分布在哪个范围内（如果有的话）表现为幂律。然而，他们的方法被发现是失败的，因为在某些情况下，真实的（模拟的）幂律尾不能被识别出来，然后幂律假设被拒绝。此外，当扩展到具有上截断的幂律分布时，该方法不能很好地工作。我们详细解释了一个类似但可选的程序，适用于截断和非截断幂律分布，基于最大似然估计，Kolmogorov-Smirnov拟合优度检验和蒙特卡罗模拟。提供了主要概念的概述以及它们的实际实现方法。我们的方法的性能在几个经验数据上进行了测试，这些数据以前是用不太系统的方法分析的。我们发现这种方法的效果非常令人满意。
Recently, Clauset, Shalizi, and Newman have proposed a systematic method to find over which range (if any) a certain distribution behaves as a power law. However, their method has been found to fail, in the sense that true (simulated) power-law tails are not recognized as such in some instances, and then the power-law hypothesis is rejected. Moreover, the method does not work well when extended to power-law distributions with an upper truncation. We explain in detail a similar but alternative procedure, valid for truncated as well as for non-truncated power-law distributions, based in maximum likelihood estimation, the Kolmogorov-Smirnov goodness-of-fit test, and Monte Carlo simulations. An overview of the main concepts as well as a recipe for their practical implementation is provided. The performance of our method is put to test on several empirical data which were previously analyzed with less systematic approaches. We find the functioning of the method very satisfactory.