The paper by Clauset, Shalizi, and Newman addresses the challenges of detecting and characterizing power-law distributions in empirical data. Power-law distributions are common in various scientific fields, but their detection is complicated by large fluctuations in the tail of the distribution and the difficulty in identifying the range over which power-law behavior holds. Common methods like least-squares fitting can produce inaccurate estimates and do not indicate whether the data follow a power law at all. The authors present a statistical framework combining maximum-likelihood fitting with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic and likelihood ratios. They evaluate the effectiveness of this approach using synthetic data and apply it to real-world data sets from different disciplines. The methods allow for accurate estimation of the scaling parameter and the lower bound on the power-law behavior, and they provide a principled way to test the plausibility of the power-law hypothesis. The paper also discusses the limitations of previous methods and highlights the importance of choosing appropriate goodness-of-fit measures.The paper by Clauset, Shalizi, and Newman addresses the challenges of detecting and characterizing power-law distributions in empirical data. Power-law distributions are common in various scientific fields, but their detection is complicated by large fluctuations in the tail of the distribution and the difficulty in identifying the range over which power-law behavior holds. Common methods like least-squares fitting can produce inaccurate estimates and do not indicate whether the data follow a power law at all. The authors present a statistical framework combining maximum-likelihood fitting with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic and likelihood ratios. They evaluate the effectiveness of this approach using synthetic data and apply it to real-world data sets from different disciplines. The methods allow for accurate estimation of the scaling parameter and the lower bound on the power-law behavior, and they provide a principled way to test the plausibility of the power-law hypothesis. The paper also discusses the limitations of previous methods and highlights the importance of choosing appropriate goodness-of-fit measures.