plfit: Fitting power-law distributions to empirical data. This program fits power-law distributions to empirical (discrete or continuous) data, according to the method of Clauset, Shalizi and Newman. Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distributions – the part of the distributions representing large but rare events – and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. We present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov - Smirnov (KS) statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data, while in others the power law is ruled out.

References in zbMATH (referenced in 239 articles , 1 standard article )

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  1. Demaine, Erik D.; Reidl, Felix; Rossmanith, Peter; F. S. Sánchez Villaamil, Fernando; Sikdar, Somnath; Sullivan, Blair D.: Structural sparsity of complex networks: bounded expansion in random models and real-world graphs (2019)
  2. Eden, Talya; Ron, Dana; Seshadhri, C.: Sublinear time estimation of degree distribution moments: the arboricity connection (2019)
  3. Ehrhardt, Beate; Wolfe, Patrick J.: Network modularity in the presence of covariates (2019)
  4. Hadlock, Christopher C.; Bickel, J. Eric: The generalized Johnson quantile-parameterized distribution system (2019)
  5. Hou, Wenpin; Ruan, Peiying; Ching, Wai-Ki; Akutsu, Tatsuya: On the number of driver nodes for controlling a Boolean network when the targets are restricted to attractors (2019)
  6. James, Richard D.: Materials from mathematics (2019)
  7. Jin, Yi; Liu, Xianhe; Song, Huibo; Zheng, Junling; Pan, Jienan: General fractal topography: an open mathematical framework to characterize and model mono-scale-invariances (2019)
  8. Kruse, Thomas; Schneider, Judith C.; Schweizer, Nikolaus: Technical note: The joint impact of (F)-divergences and reference models on the contents of uncertainty sets (2019)
  9. Lawless, Caroline; Arbel, Julyan: A simple proof of Pitman-Yor’s Chinese restaurant process from its stick-breaking representation (2019)
  10. Li, Cheng; Lin, Lizhen; Dunson, David B.: On posterior consistency of tail index for Bayesian kernel mixture models (2019)
  11. Li, Jing; Jin, Zhen; Yuan, Yuan: Effect of adaptive rewiring delay in an SIS network epidemic model (2019)
  12. Lipan, Ovidiu; Wu, Emily: A stochastic switch with different phases (2019)
  13. Rovira Kaltwasser, Pablo; Spelta, Alessandro: Identifying systemically important financial institutions: a network approach (2019)
  14. Wang, Tiandong; Resnick, Sidney I.: Consistency of Hill estimators in a linear preferential attachment model (2019)
  15. Wu, F. Y.; Lin, P.; Gao, D. L.; Wang, Z. K.; Wang, K. H.; Ma, J.: An experimental study of exit position on escape efficiency using mice under competition (2019)
  16. Zhao, Dazhi; Luo, Maokang: Representations of acting processes and memory effects: general fractional derivative and its application to theory of heat conduction with finite wave speeds (2019)
  17. Zhu, Xuening; Chang, Xiangyu; Li, Runze; Wang, Hansheng: Portal nodes screening for large scale social networks (2019)
  18. Alvarez-Martinez, Roberto; Cocho, Germinal; Martinez-Mekler, Gustavo: Rank ordered beta distributions of nonlinear map symbolic dynamics families with a first-order transition between dynamical regimes (2018)
  19. Bandyopadhyay, Abhirup; Kar, Samarjit: Impact of network structure on synchronization of Hindmarsh-Rose neurons coupled in structured network (2018)
  20. Barbosa, Hugo; Barthelemy, Marc; Ghoshal, Gourab; James, Charlotte R.; Lenormand, Maxime; Louail, Thomas; Menezes, Ronaldo; Ramasco, José J.; Simini, Filippo; Tomasini, Marcello: Human mobility: models and applications (2018)

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