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 269 articles , 1 standard article )

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  1. Fazli, MohammadAmin; Ghodsi, Mohammad; Habibi, Jafar; Jalaly, Pooya; Mirrokni, Vahab; Sadeghian, Sina: On non-progressive spread of influence through social networks (2014)
  2. Hartley, Caroline; Taylor, Timothy J.; Kiss, Istvan Z.; Farmer, Simon F.; Berthouze, Luc: Identification of criticality in neuronal avalanches. II: A theoretical and empirical investigation of the driven case (2014)
  3. Li, Hui; Hao, Li-Ying; Chen, Rong; Ge, Xin; Zhao, Hai: Symmetric preferential attachment for new vertices attaching to software networks (2014) ioport
  4. Liu, Xiao Fan; Tse, Chi Kong: Impact of degree mixing pattern on consensus formation in social networks (2014)
  5. Perkins, Will; Tygert, Mark; Ward, Rachel: Some deficiencies of (\chi^2) and classical exact tests of significance (2014)
  6. Ruiz Vargas, E.; Mitchell, D. G. V.; Greening, S. G.; Wahl, L. M.: Topology of whole-brain functional MRI networks: improving the truncated scale-free model (2014)
  7. Sommer, Christian: Shortest-path queries in static networks (2014)
  8. Stella, Massimo; Brede, Markus: A (\kappa)-deformed model of growing complex networks with fitness (2014)
  9. Teteryatnikova, Mariya: Systemic risk in banking networks: advantages of “tiered” banking systems (2014)
  10. Virkar, Yogesh; Clauset, Aaron: Power-law distributions in binned empirical data (2014)
  11. Wahid, Alif; Leckie, Christopher; Zhou, Chenfeng: Estimating the number of hosts corresponding to an intrusion alert while preserving privacy (2014)
  12. Wang, Long; Ma, Yinghong: Structure properties of one-mode collaboration network model based on rate equation approach (2014)
  13. Yang, Guang; Zheng, Wenzhi; Huang, Jiping: Partial information, market efficiency, and anomalous continuous phase transition (2014)
  14. Yao, Can-Zhong; Lin, Ji-Nan; Liu, Xiao-Feng; Zheng, Xu-Zhou: Dynamic features analysis for the large-scale logistics system warehouse-out operation (2014)
  15. Zipkin, Elise F.; Leirness, Jeffery B.; Kinlan, Brian P.; O’Connell, Allan F.; Silverman, Emily D.: Fitting statistical distributions to sea duck count data: implications for survey design and abundance estimation (2014)
  16. Aranda-Corral, Gonzalo A.; Borrego-Díaz, Joaquín; Galán-Páez, Juan: Complex concept lattices for simulating human prediction in sport (2013)
  17. Buccafurri, Francesco; Foti, Vincenzo Daniele; Lax, Gianluca; Nocera, Antonino; Ursino, Domenico: Bridge analysis in a social internetworking scenario (2013) ioport
  18. Cirillo, Pasquale: Are your data really Pareto distributed? (2013)
  19. Clauset, Aaron; Woodard, Ryan: Estimating the historical and future probabilities of large terrorist events (2013)
  20. Clauset, Aaron; Woodard, Ryan: Rejoinder of “Estimating the historical and future probabilities of large terrorist events” by Aaron Clauset and Ryan Woodard (2013)

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