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. Clote, P.: Are RNA networks scale-free? (2020)
  2. Comin, Cesar H.; Peron, Thomas; Silva, Filipi N.; Amancio, Diego R.; Rodrigues, Francisco A.; Costa, Luciano da F.: Complex systems: features, similarity and connectivity (2020)
  3. Dave, Chetan; Sorge, Marco M.: Sunspot-driven fat tails: a note (2020)
  4. Duarte-López, Ariel; Pérez-Casany, Marta; Valero, Jordi: The Zipf-Poisson-stopped-sum distribution with an application for modeling the degree sequence of social networks (2020)
  5. Eliazar, Iddo; Giorgi, Giovanni M.: From Gini to Bonferroni to Tsallis: an inequality-indices trek (2020)
  6. Grilli, Ruggero; Tedeschi, Gabriele; Gallegati, Mauro: Business fluctuations in a behavioral switching model: gridlock effects and credit crunch phenomena in financial networks (2020)
  7. Halvarsson, Daniel: Maximum likelihood estimation of asymmetric double type II Pareto distributions (2020)
  8. Lehtomaa, Jaakko; Resnick, Sidney I.: Asymptotic independence and support detection techniques for heavy-tailed multivariate data (2020)
  9. Niu, Min; Li, Ruixia: The average weighted path length for a class of hierarchical networks (2020)
  10. Pachon, Angelica; Polito, Federico; Sacerdote, Laura: On the continuous-time limit of the Barabási-Albert random graph (2020)
  11. Pesaran, M. Hashem; Yang, Cynthia Fan: Econometric analysis of production networks with dominant units (2020)
  12. Puente-Ajovín, Miguel; Ramos, Arturo; Sanz-Gracia, Fernando; Arribas-Bel, Daniel: How sensitive is city size distribution to the definition of city? The case of Spain (2020)
  13. Seres, István András; Gulyás, László; Nagy, Dániel A.; Burcsi, Péter: Topological analysis of Bitcoin’s lightning network (2020)
  14. Song, Yangbo; van der Schaar, Mihaela: Dynamic network formation with foresighted agents (2020)
  15. Wang, Tiandong; Resnick, Sidney I.: Degree growth rates and index estimation in a directed preferential attachment model (2020)
  16. Wan, Phyllis; Wang, Tiandong; Davis, Richard A.; Resnick, Sidney I.: Are extreme value estimation methods useful for network data? (2020)
  17. Zhu, Xuening; Huang, Danyang; Pan, Rui; Wang, Hansheng: Multivariate spatial autoregressive model for large scale social networks (2020)
  18. Zhu, Xuening; Pan, Rui: Grouped network vector autoregression (2020)
  19. Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Zhao, Yufei: An (L^p) theory of sparse graph convergence. I: Limits, sparse random graph models, and power law distributions (2019)
  20. Bricker, Jesse; Hansen, Peter; Volz, Alice Henriques: Wealth concentration in the U.S. after augmenting the upper tail of the survey of consumer finances (2019)

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