plfit 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; SNAP; Gephi; KONECT; QRM; ismev; GitHub; Powerlaw; igraph; Arc_Mat; STABLE; GraphBase; longmemo; Brain Connectivity Toolbox; KronFit; wmtsa; GenLouvain; TRANSFAC Cited in: 293 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Power-law distributions in empirical data. Zbl 1176.62001Clauset, Aaron; Shalizi, Cosma Rohilla; Newman, M. E. J. 2009 all top 5 Cited by 732 Authors 5 Huang, DanYang 5 Resnick, Sidney Ira 5 Wang, Hansheng 5 Wang, Tiandong 5 Zhou, Weixing 4 Clauset, Aaron 4 Jiang, Zhiqiang 3 Comin, César Henrique 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 Duarte-López, Ariel 2 Friedrich, Tobias 2 Fulger, Daniel 2 Germano, Guido 2 Guan, Shuguang 2 Hu, Wei 2 Jing, Bingyi 2 Johnson, Joseph D. 2 Johnson, Neil F. 2 Kanoria, Mridula 2 Korutcheva, Elka R. 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 Nikitina, E. Y. 2 Ortega, Diego 2 Pan, Rui 2 Pérez-Casany, Marta 2 Petronio, Filomena 2 Podobnik, Boris 2 Porter, Michael D. 2 Radillo-Ochoa, Diego 2 Reynolds, Andy M. 2 Rodríguez-Laguna, Javier 2 Rossmanith, Peter 2 Scalas, Enrico 2 Silva, Filipi Nascimento 2 Small, Michael 2 Stanley, H. Eugene 2 Sur, Abhik 2 Terrero-Escalante, César A. 2 Tichý, Tomáš 2 Tong, Jinying 2 Trapani, Lorenzo 2 Valero, Jordi 2 White, Gentry 2 Woodard, Ryan 2 Yudin, E. B. 2 Zhang, Bo 2 Zhang, Rong 2 Zhang, Zhenzhong 2 Zhao, Dazhi 2 Zhou, Jing 2 Zou, Yong 1 Abdulali, Arsen 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 Annila, Arto 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. ...and 632 more Authors all top 5 Cited in 115 Serials 41 Physica A 12 Journal of Statistical Mechanics: Theory and Experiment 11 Chaos, Solitons and Fractals 11 Journal of Theoretical Biology 10 The Annals of Applied Statistics 8 Quantitative Finance 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 Theoretical Computer Science 5 Electronic Journal of Statistics 4 Journal of Econometrics 4 Economics Letters 4 SIAM Review 4 Chaos 4 Networks and Spatial Economics 3 Physics Letters. 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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 ...and 15 more Serials all top 5 Cited in 29 Fields 102 Statistics (62-XX) 99 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 50 Probability theory and stochastic processes (60-XX) 49 Combinatorics (05-XX) 38 Biology and other natural sciences (92-XX) 36 Statistical mechanics, structure of matter (82-XX) 34 Operations research, mathematical programming (90-XX) 28 Computer science (68-XX) 10 Dynamical systems and ergodic theory (37-XX) 10 Information and communication theory, circuits (94-XX) 8 Numerical analysis (65-XX) 7 Systems theory; control (93-XX) 5 Mechanics of deformable solids (74-XX) 4 Measure and integration (28-XX) 3 Ordinary differential equations (34-XX) 3 Partial differential equations (35-XX) 3 Geophysics (86-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Fluid mechanics (76-XX) 1 History and biography (01-XX) 1 Number theory (11-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Algebraic topology (55-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX) 1 Mathematics education (97-XX) Citations by Year