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Problems with fitting to the power-law distribution

The European Physical Journal B - Condensed Matter and Complex Systems volume 41, pages 255–258 (2004)Cite this article

Abstract.

This short communication uses a simple experiment to show that fitting to a power law distribution by using graphical methods based on linear fit on the log-log scale is biased and inaccurate. It shows that using maximum likelihood estimation (MLE) is far more robust. Finally, it presents a new table for performing the Kolmogorov-Smirnov test for goodness-of-fit tailored to power-law distributions in which the power-law exponent is estimated using MLE. The techniques presented here will advance the application of complex network theory by allowing reliable estimation of power-law models from data and further allowing quantitative assessment of goodness-of-fit of proposed power-law models to empirical data.

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References

  1. R. Albert, H. Jeong, A.-L. Barabási, Nature 401, 130 (1999)

    Article  Google Scholar 

  2. H. Jeong, B. Tombor, R. Albert, Z.N. Oltval, A.-L. Barabási, Nature 407, 651 (2000)

    Article  CAS  PubMed  Google Scholar 

  3. M. Faloutsos, P. Faloutsos, C. Faloutsos, Computer Commun. Rev. 29, 251 (1999)

    Google Scholar 

  4. S. Redner, Eur. Phys. J. B 4, 131 (1998)

    Article  Google Scholar 

  5. F. Liljeros, C.R. Edling, L.A.N. Amaral, H.E. Stanley, Y. Aberg, Nature 411, 907 (2001)

    Article  Google Scholar 

  6. N.L. Johnson, S. Kotz, A.W. Kemp, Univariate discrete distributions (John Wiley & Sons, New York, 1992)

  7. J.-L. Guilleaume, M. Latapy, Information Processing Lett. 90, 215 (2004)

    Article  Google Scholar 

  8. R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002)

    Article  MathSciNet  Google Scholar 

  9. M.E.J. Newman, SIAM Rev. 45, 157 (2003)

    Google Scholar 

  10. J.H. Jones, M.S. Handcock, Proc. Royal Soc. London Series B-Biological Sciences 270, 1123 (2003)

    Article  Google Scholar 

  11. J. Park, M.E.J. Newman, Phys. Rev. E 68, 036122 (2003)

    Article  Google Scholar 

  12. A. Walther, Acta Mathematica 48, 393 (1926)

    MATH  Google Scholar 

  13. P.T. Nicholls, J. Am. Soc. Information Sci. 40, 379 (1989)

    Google Scholar 

  14. A.N. Kolmogorov, Giornale dell’ Instituto Italiano degli Attuari 4, 77 (1933)

    Google Scholar 

  15. M.L. Pao, Information Processing and Management 21, 305 (1985)

    Article  Google Scholar 

  16. W.J. Conover, Practical nonparametric statistics (Wiley, New York, 1999)

  17. H.W. Lilifoers, J. Am. Stat. Asso. 62, 399 (1967)

    Google Scholar 

  18. H.W. Lilifoers, J. Am. Stat. Asso. 64, 387 (1969)

    Google Scholar 

  19. A.J. Lotka, J. Washington Academy of Sciences 16, 317 (1926)

    Google Scholar 

Download references

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Authors and Affiliations

  1. School of Electrical and Computer Engineering, Oklahoma State University, OK 74078, Stillwater, USA

    M. L. Goldstein, S. A. Morris & G. G. Yen

Authors
  1. M. L. Goldstein
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  2. S. A. Morris
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  3. G. G. Yen
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Corresponding author

Correspondence to G. G. Yen.

Additional information

Received: 18 June 2004, Published online: 12 October 2004

PACS:

02.50.Ng Distribution theory and Monte Carlo studies - 05.10.Ln Monte Carlo methods - 89.75.-k Complex systems

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Goldstein, M.L., Morris, S.A. & Yen, G.G. Problems with fitting to the power-law distribution. Eur. Phys. J. B 41, 255–258 (2004). https://doi.org/10.1140/epjb/e2004-00316-5

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  • DOI: https://doi.org/10.1140/epjb/e2004-00316-5

Keywords

  • Empirical Data
  • Maximum Likelihood Estimation
  • Likelihood Estimation
  • Complex Network
  • Reliable Estimation