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. Garcia Garcia, Juan Manuel: A fixed-point algorithm to estimate the Yule-Simon distribution parameter (2011)
  2. Li, Wentian: On parameters of the human genome (2011)
  3. Mora, Thierry; Bialek, William: Are biological systems poised at criticality? (2011)
  4. Ribeiro, Leonardo Andrade; Härder, Theo: Generalizing prefix filtering to improve set similarity joins (2011) ioport
  5. Selvam, A. M.: Signatures of universal characteristics of fractal fluctuations in global mean monthly temperature anomalies (2011)
  6. Turnu, I.; Concas, G.; Marchesi, M.; Pinna, S.; Tonelli, R.: A modified Yule process to model the evolution of some object-oriented system properties (2011) ioport
  7. Zweig, Katharina A.: Good versus optimal: why network analytic methods need more systematic evaluation (2011) ioport
  8. Concas, Giulio; Marchesi, Michele; Murgia, Alessandro; Tonelli, Roberto: An empirical study of social networks metrics in object-oriented software (2010) ioport
  9. James, Alex; Pitchford, Jonathan W.; Plank, Michael J.: Efficient or inaccurate? Analytical and numerical modelling of random search strategies (2010)
  10. Maillart, T.; Sornette, D.: Heavy-tailed distribution of cyber-risks (2010)
  11. Politi, M.; Scalas, E.; Fulger, D.; Germano, G.: Spectral densities of Wishart-Lévy free stable random matrices (2010)
  12. Sator, N.; Hietala, H.: Damage in impact fragmentation (2010)
  13. Zhang, Jiang; Guo, Liangpeng: Scaling behaviors of weighted food webs as energy transportation networks (2010)
  14. Brenes, David J.; Gayo-Avello, Daniel: Stratified analysis of AOL query log (2009) ioport
  15. Clauset, Aaron; Shalizi, Cosma Rohilla; Newman, M. E. J.: Power-law distributions in empirical data (2009)
  16. Hecker, Michael; Goertsches, Robert Hermann; Engelmann, Robby; Thiesen, Hans-Jürgen; Guthke, Reinhard: Integrative modeling of transcriptional regulation in response to antirheumatic therapy (2009) ioport
  17. Klimek, Peter; Thurner, Stefan; Hanel, Rudolf: Pruning the tree of life: (k)-core percolation as selection mechanism (2009)
  18. Ni, Xiao-Hui; Jiang, Zhi-Qiang; Zhou, Wei-Xing: Degree distributions of the visibility graphs mapped from fractional Brownian motions and multifractal random walks (2009)
  19. Gnutzmann, Hinnerk: Network formation under cumulative advantage: Evidence from the Cambridge high-tech cluster (2008)

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