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Applications of the generalized law of Benford to informetric data

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  • Leo Egghe
  • Raf Guns

Abstract

In a previous work (Egghe, 2011), the first author showed that Benford's law (describing the logarithmic distribution of the numbers 1, 2, … , 9 as first digits of data in decimal form) is related to the classical law of Zipf with exponent 1. The work of Campanario and Coslado (2011), however, shows that Benford's law does not always fit practical data in a statistical sense. In this article, we use a generalization of Benford's law related to the general law of Zipf with exponent β > 0. Using data from Campanario and Coslado, we apply nonlinear least squares to determine the optimal β and show that this generalized law of Benford fits the data better than the classical law of Benford.

Suggested Citation

  • Leo Egghe & Raf Guns, 2012. "Applications of the generalized law of Benford to informetric data," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 63(8), pages 1662-1665, August.
    • Handle: RePEc:bla:jamist:v:63:y:2012:i:8:p:1662-1665
    DOI: 10.1002/asi.22690
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    Citations

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    Cited by:

    1. M. Jayasree & C. S. Pavana Jyothi & P. Ramya, 2018. "Benford’s Law and Stock Market—The Implications for Investors: The Evidence from India Nifty Fifty," Jindal Journal of Business Research, , vol. 7(2), pages 103-121, December.
    2. Alexandre Donizeti Alves & Horacio Hideki Yanasse & Nei Yoshihiro Soma, 2014. "Benford’s Law and articles of scientific journals: comparison of JCR® and Scopus data," Scientometrics, Springer;Akadémiai Kiadó, vol. 98(1), pages 173-184, January.
    3. Whyman, G. & Ohtori, N. & Shulzinger, E. & Bormashenko, Ed., 2016. "Revisiting the Benford law: When the Benford-like distribution of leading digits in sets of numerical data is expectable?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 595-601.
    4. Egghe, L., 2013. "The functional relation between the impact factor and the uncitedness factor revisited," Journal of Informetrics, Elsevier, vol. 7(1), pages 183-189.
    5. Druică, Elena & Oancea, Bogdan & Vâlsan, Călin, 2018. "Benford's law and the limits of digit analysis," International Journal of Accounting Information Systems, Elsevier, vol. 31(C), pages 75-82.
    6. Barabesi, Lucio & Pratelli, Luca, 2020. "On the Generalized Benford law," Statistics & Probability Letters, Elsevier, vol. 160(C).
    7. Hsiang-chi Tseng & Wei-neng Huang & Ding-wei Huang, 2017. "Modified Benford’s law for two-exponent distributions," Scientometrics, Springer;Akadémiai Kiadó, vol. 110(3), pages 1403-1413, March.
    8. Mir, T.A., 2014. "The Benford law behavior of the religious activity data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 408(C), pages 1-9.

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