swMATH ID: 23186
Software Authors: Clauset A, Shalizi CR, Newman MEJ
Description: 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.
Homepage: https://github.com/ntamas/plfit
Source Code: https://github.com/ntamas/plfit
Related Software: bootstrap; R; poweRlaw; Gephi; SNAP; Powerlaw; igraph; GitHub; KONECT; ismev; QRM; STABLE; GraphBase; Arc_Mat; longmemo; zipfextR; fitdistrplus; Matlab; KronFit; AlexNet
Cited in: 267 Publications
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Cited by 665 Authors

5 Resnick, Sidney Ira
5 Zhou, Weixing
4 Clauset, Aaron
4 Huang, DanYang
4 Jiang, Zhiqiang
4 Wang, Hansheng
4 Wang, Tiandong
3 Gallegati, Mauro
3 Ibrahim, Kamarulzaman
3 Masseran, Nurulkamal
3 Safari, Muhammad Aslam Mohd
3 Zhu, Xuening
2 Abrams, Daniel M.
2 Bandyopadhyay, Abhirup
2 Bargigli, Leonardo
2 Bhamidi, Shankar
2 Cai, Shimin
2 Canabarro, Askery
2 Caron, François
2 Chang, Xiangyu
2 Chattopadhyay, Swarup
2 Cirillo, Pasquale
2 Cocho, Germinal
2 Comin, César Henrique
2 Duarte-López, Ariel
2 Friedrich, Tobias
2 Fulger, Daniel
2 Germano, Guido
2 Johnson, Joseph D.
2 Johnson, Neil F.
2 Kanoria, Mridula
2 Krohmer, Anton
2 Lando, Tommaso
2 Li, Wentian
2 Lillo, Felipe
2 Luo, Maokang
2 Mandel, Antoine
2 Marsili, Matteo
2 Murthy, Chivukula A.
2 Pan, Rui
2 Pérez-Casany, Marta
2 Petronio, Filomena
2 Podobnik, Boris
2 Porter, Michael D.
2 Reynolds, Andy M.
2 Scalas, Enrico
2 Small, Michael
2 Stanley, H. Eugene
2 Sur, Abhik
2 Tichý, Tomáš
2 Tong, Jinying
2 Trapani, Lorenzo
2 Valero, Jordi
2 White, Gentry
2 Woodard, Ryan
2 Yudin, E. B.
2 Zhang, Zhenzhong
2 Zhao, Dazhi
1 Abel, William
1 Abid, Muhammad
1 Adams, Henry
1 Adenso-Díaz, Belarmino
1 Aiello, Marco
1 Aksoy, Sinan G.
1 Akutsu, Tatsuya
1 Alvarez-Martinez, Roberto
1 Alvarez, Emiliano
1 Álvarez, Nicanor García
1 Amancio, Diego R.
1 Aminian, Manuchehr
1 Anand, Abhinav
1 Anand, Madhur
1 Antal, Tibor
1 Antonio, Katrien
1 Antunes, Nelson
1 Anwar, Raheel
1 Aranda-Corral, Gonzalo A.
1 Arbel, Julyan
1 Ardekani, Aref Mahdavi
1 Arribas-Bel, Daniel
1 Aste, Tomaso
1 Ayed, Fadhel
1 Badescu, Andrei L.
1 Badhwar, Rahul
1 Baek, Seung Ki
1 Bagler, Ganesh
1 Bakouie, Fatemeh
1 Barbosa, Hugo
1 Barigozzi, Matteo
1 Barthelemy, Marc
1 Basu, Sankar
1 Batagelj, Vladimir
1 Battiston, Marco
1 Bauch, Chris T.
1 Beare, Brendan K.
1 Bergmann, Katharina
1 Bernhardsson, Sebastian
1 Berthouze, Luc
1 Best, Janet A.
1 Bhattacharjee, Chinmoy
...and 565 more Authors
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Cited in 112 Serials

35 Physica A
12 Journal of Statistical Mechanics: Theory and Experiment
10 The Annals of Applied Statistics
10 Journal of Theoretical Biology
8 Quantitative Finance
7 Chaos, Solitons and Fractals
7 Communications in Nonlinear Science and Numerical Simulation
6 Journal of Statistical Physics
6 Journal of Economic Dynamics & Control
5 Applied Mathematics and Computation
5 Electronic Journal of Statistics
4 Journal of Econometrics
4 Theoretical Computer Science
4 Economics Letters
4 SIAM Review
4 Chaos
4 Networks and Spatial Economics
3 Physics Letters. A
3 Physics Reports
3 Information Sciences
3 New Journal of Physics
3 Journal of Systems Science and Complexity
2 Bulletin of Mathematical Biology
2 Journal of Computer and System Sciences
2 Journal of Mathematical Psychology
2 The Journal of Mathematical Sociology
2 Statistics & Probability Letters
2 Physica D
2 Machine Learning
2 Communications in Statistics. Theory and Methods
2 European Journal of Operational Research
2 Stochastic Processes and their Applications
2 Computational Statistics and Data Analysis
2 Computational Economics
2 Journal of Applied Statistics
2 Extremes
2 Journal of Machine Learning Research (JMLR)
2 Mathematical Biosciences and Engineering
2 Waves in Random and Complex Media
2 The European Physical Journal B. Condensed Matter and Complex Systems
2 Advances in Mathematical Physics
2 Decision Analysis
2 Dependence Modeling
2 SIAM Journal on Mathematics of Data Science
1 ACM Computing Surveys
1 Advances in Applied Probability
1 Discrete Applied Mathematics
1 Journal of Mathematical Biology
1 Computing
1 International Journal of Game Theory
1 Journal of Computational and Applied Mathematics
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1 Journal of Statistical Planning and Inference
1 Mathematica Slovaca
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1 SIAM Journal on Control and Optimization
1 Theoretical Population Biology
1 Transactions of the American Mathematical Society
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1 Insurance Mathematics & Economics
1 Econometric Reviews
1 Asia-Pacific Journal of Operational Research
1 SIAM Journal on Discrete Mathematics
1 European Journal of Applied Mathematics
1 Neural Computation
1 The Annals of Applied Probability
1 Journal of Global Optimization
1 Automation and Remote Control
1 Journal of Elasticity
1 Journal of Statistical Computation and Simulation
1 Bulletin of the American Mathematical Society. New Series
1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
1 Applied and Computational Harmonic Analysis
1 Fractals
1 The Electronic Journal of Combinatorics
1 Statistica Sinica
1 Complexity
1 Bernoulli
1 ELA. The Electronic Journal of Linear Algebra
1 Journal of Nonparametric Statistics
1 Nonlinear Dynamics
1 Soft Computing
1 Journal of Combinatorial Optimization
1 Discrete Mathematics and Theoretical Computer Science. DMTCS
1 Wuhan University Journal of Natural Sciences (WUJNS)
1 Fractional Calculus & Applied Analysis
1 Journal of the Royal Statistical Society. Series B. Statistical Methodology
1 Discrete Dynamics in Nature and Society
1 Journal of Biological Systems
1 Methodology and Computing in Applied Probability
1 Discrete and Continuous Dynamical Systems. Series B
1 ASTIN Bulletin
1 SIAM Journal on Applied Dynamical Systems
1 Statistical Applications in Genetics and Molecular Biology
1 Computational Management Science
1 International Journal of Fracture
1 Sibirskie Èlektronnye Matematicheskie Izvestiya
1 Stochastics
1 Statistical Methodology
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