This paper presents a principled statistical framework for detecting and quantifying power-law behavior in empirical data. The authors propose a method combining maximum-likelihood fitting with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic and likelihood ratios. They evaluate this approach using synthetic data and apply it to 24 real-world datasets from various disciplines. The method allows for accurate estimation of power-law parameters and provides a way to determine whether the data follow a power law. The authors also discuss the importance of correctly identifying the lower bound of the power-law region and the challenges of distinguishing power-law behavior from other distributions. The paper highlights the limitations of common methods like least-squares fitting and emphasizes the need for rigorous statistical tests to validate power-law hypotheses. The authors conclude that while power-law distributions are common in many scientific phenomena, their detection requires careful analysis and that the proposed methods provide a reliable way to assess the validity of power-law fits.This paper presents a principled statistical framework for detecting and quantifying power-law behavior in empirical data. The authors propose a method combining maximum-likelihood fitting with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic and likelihood ratios. They evaluate this approach using synthetic data and apply it to 24 real-world datasets from various disciplines. The method allows for accurate estimation of power-law parameters and provides a way to determine whether the data follow a power law. The authors also discuss the importance of correctly identifying the lower bound of the power-law region and the challenges of distinguishing power-law behavior from other distributions. The paper highlights the limitations of common methods like least-squares fitting and emphasizes the need for rigorous statistical tests to validate power-law hypotheses. The authors conclude that while power-law distributions are common in many scientific phenomena, their detection requires careful analysis and that the proposed methods provide a reliable way to assess the validity of power-law fits.