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Parameter estimation for power-law distributions by maximum likelihood methods

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  • H. Bauke

Abstract

Distributions following a power-law are an ubiquitous phenomenon. Methods for determining the exponent of a power-law tail by graphical means are often used in practice but are intrinsically unreliable. Maximum likelihood estimators for the exponent are a mathematically sound alternative to graphical methods. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Suggested Citation

  • H. Bauke, 2007. "Parameter estimation for power-law distributions by maximum likelihood methods," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 58(2), pages 167-173, July.
    • Handle: RePEc:spr:eurphb:v:58:y:2007:i:2:p:167-173
    DOI: 10.1140/epjb/e2007-00219-y
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    2. Kwame Boamah‐Addo & Tomasz J. Kozubowski & Anna K. Panorska, 2023. "A discrete truncated Zipf distribution," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(2), pages 156-187, May.
    3. Tunnicliffe, Martin & Hunter, Gordon, 2022. "Random sampling of the Zipf–Mandelbrot distribution as a representation of vocabulary growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).
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    5. Restocchi, Valerio & McGroarty, Frank & Gerding, Enrico, 2019. "The stylized facts of prediction markets: Analysis of price changes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 159-170.
    6. Mikail Rubinov & Olaf Sporns & Jean-Philippe Thivierge & Michael Breakspear, 2011. "Neurobiologically Realistic Determinants of Self-Organized Criticality in Networks of Spiking Neurons," PLOS Computational Biology, Public Library of Science, vol. 7(6), pages 1-14, June.
    7. Yinpeng Liu & Xiangyun Gao & Jianfeng Guo, 2018. "Network Features of the EU Carbon Trade System: An Evolutionary Perspective," Energies, MDPI, vol. 11(6), pages 1-16, June.
    8. Yan, Qiang & Wu, Lianren & Zheng, Lan, 2013. "Social network based microblog user behavior analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(7), pages 1712-1723.
    9. Alonso Rodríguez-Navarro & Ricardo Brito, 2019. "Probability and expected frequency of breakthroughs: basis and use of a robust method of research assessment," Scientometrics, Springer;Akadémiai Kiadó, vol. 119(1), pages 213-235, April.
    10. Dieter Hendricks & Tim Gebbie & Diane Wilcox, 2015. "Detecting intraday financial market states using temporal clustering," Papers 1508.04900, arXiv.org, revised Feb 2017.
    11. Restocchi, Valerio & McGroarty, Frank & Gerding, Enrico, 2019. "Statistical properties of volume and calendar effects in prediction markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1150-1160.
    12. Tomson Ogwang, 2011. "Power laws in top wealth distributions: evidence from Canada," Empirical Economics, Springer, vol. 41(2), pages 473-486, October.
    13. Todorova, Lora & Vogt, Bodo, 2011. "Power law distribution in high frequency financial data? An econometric analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4433-4444.
    14. Ogwang, Tomson, 2013. "Is the wealth of the world’s billionaires Paretian?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 757-762.
    15. Pană, Gabriel Tiberiu & Nicolin-Żaczek, Alexandru, 2023. "Motifs in earthquake networks: Romania, Italy, United States of America, and Japan," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    16. Amancio, Diego R. & Nunes, Maria G.V. & Oliveira, Osvaldo N. & Costa, Luciano da F., 2012. "Extractive summarization using complex networks and syntactic dependency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1855-1864.
    17. Rashidisabet, Homa & Ajilore, Olusola & Leow, Alex & Demos, Alexander P., 2022. "Revisiting power-law estimation with applications to real-world human typing dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    18. Amancio, Diego Raphael & Oliveira, Osvaldo Novais & da Fontoura Costa, Luciano, 2012. "Three-feature model to reproduce the topology of citation networks and the effects from authors’ visibility on their h-index," Journal of Informetrics, Elsevier, vol. 6(3), pages 427-434.
    19. Guillen, Montserrat & Prieto, Faustino & Sarabia, José María, 2011. "Modelling losses and locating the tail with the Pareto Positive Stable distribution," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 454-461.
    20. Ricardo González-López & Javier B. Gómez & Amalio F. Pacheco, 2020. "A Minimal Agent-Based Model For The Size-Frequency Distribution Of Firms," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 23(01), pages 1-27, March.
    21. Wang, Shengfeng & Feng, Xin & Wu, Ye & Xiao, Jinhua, 2017. "Double dynamic scaling in human communication dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 313-318.
    22. Anton Kolotilin & Valentyn Panchenko, 2018. "Estimation of a Scale-Free Network Formation Model," Discussion Papers 2018-10, School of Economics, The University of New South Wales.
    23. Junho Na & Jeong-dong Lee & Chulwoo Baek, 2017. "Is the service sector different in size heterogeneity?," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 12(1), pages 95-120, April.
    24. Coronel-Brizio, H.F. & Hernández-Montoya, A.R., 2010. "The Anderson–Darling test of fit for the power-law distribution from left-censored samples," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3508-3515.
    25. repec:hal:journl:dumas-00807765 is not listed on IDEAS

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