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 230 articles , 1 standard article )

Showing results 1 to 20 of 230.
Sorted by year (citations)

1 2 3 ... 10 11 12 next

  1. Farahbakhsh, Isaiah; Bauch, Chris T.; Anand, Madhur: Best response dynamics improve sustainability and equity outcomes in common-pool resources problems, compared to imitation dynamics (2021)
  2. Johnson, Joseph D.; White, Nathan L.; Kangabire, Alain; Abrams, Daniel M.: A dynamical model for the origin of anisogamy (2021)
  3. Naik, Cian; Caron, François; Rousseau, Judith: Sparse networks with core-periphery structure (2021)
  4. Naulet, Zacharie; Roy, Daniel M.; Sharma, Ekansh; Veitch, Victor: Bootstrap estimators for the tail-index and for the count statistics of graphex processes (2021)
  5. Nie, Wei-Peng; Zhao, Zhi-Dan; Cai, Shi-Min; Zhou, Tao: Understanding the urban mobility community by taxi travel trajectory (2021)
  6. Omelchenko, Oleksii; Bulatov, Andrei A.: Satisfiability threshold for power law random 2-SAT in configuration model (2021)
  7. Wang, Sulian; Wang, Chen: Quantile judgments of lognormal losses: an experimental investigation (2021)
  8. Adams, Henry; Aminian, Manuchehr; Farnell, Elin; Kirby, Michael; Mirth, Joshua; Neville, Rachel; Peterson, Chris; Shonkwiler, Clayton: A fractal dimension for measures via persistent homology (2020)
  9. Alvarez, Emiliano; London, Silvia: Emerging patterns in inflation expectations with multiple agents (2020)
  10. Anwar, Raheel; Yousuf, Muhammad Irfan; Abid, Muhammad: Analysis of a model for generating weakly scale-free networks (2020)
  11. Ardekani, Aref Mahdavi; Distinguin, Isabelle; Tarazi, Amine: Do banks change their liquidity ratios based on network characteristics? (2020)
  12. Bandyopadhyay, Abhirup; Dhar, Amit Kumar; Basu, Sankar: Graph coloring: a novel heuristic based on trailing path-properties, perspective and applications in structured networks (2020)
  13. Chen, Xiaolong; Gong, Kai; Wang, Ruijie; Cai, Shimin; Wang, Wei: Effects of heterogeneous self-protection awareness on resource-epidemic coevolution dynamics (2020)
  14. Clote, P.: Are RNA networks scale-free? (2020)
  15. 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)
  16. Dave, Chetan; Sorge, Marco M.: Sunspot-driven fat tails: a note (2020)
  17. 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)
  18. Eliazar, Iddo; Giorgi, Giovanni M.: From Gini to Bonferroni to Tsallis: an inequality-indices trek (2020)
  19. Grilli, Ruggero; Tedeschi, Gabriele; Gallegati, Mauro: Business fluctuations in a behavioral switching model: gridlock effects and credit crunch phenomena in financial networks (2020)
  20. Halvarsson, Daniel: Maximum likelihood estimation of asymmetric double type II Pareto distributions (2020)

1 2 3 ... 10 11 12 next