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Benford’s Law applies to word frequency rank in English, German, French, Spanish, and Italian

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  • Jennifer Golbeck

Abstract

Benford’s Law states that, in many real-world data sets, the frequency of numbers’ first digits is predicted by the formula log(1 + (1/d)). Numbers beginning with a 1 occur roughly 30% of the time, and are six times more common than numbers beginning with a 9. We show that Benford’s Law applies to the the frequency rank of words in English, German, French, Spanish, and Italian. We calculated the frequency rank of words in the Google Ngram Viewer corpora. Then, using the first significant digit of the frequency rank, we found the FSD distribution adhered to the expected Benford’s Law distribution. Over a series of additional corpora from sources ranging from news to books to social media and across the languages studied, we consistently found adherence to Benford’s Law. Furthermore, at the user-level on social media, we found Benford’s Law holds for the vast majority of users’ collected posts and significant deviations from Benford’s Law tends to be a mark of spam bots.

Suggested Citation

  • Jennifer Golbeck, 2023. "Benford’s Law applies to word frequency rank in English, German, French, Spanish, and Italian," PLOS ONE, Public Library of Science, vol. 18(9), pages 1-12, September.
    • Handle: RePEc:plo:pone00:0291337
    DOI: 10.1371/journal.pone.0291337
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    References listed on IDEAS

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    1. Andreas Diekmann, 2007. "Not the First Digit! Using Benford's Law to Detect Fraudulent Scientif ic Data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(3), pages 321-329.
    2. David Giles, 2007. "Benford's law and naturally occurring prices in certain ebaY auctions," Applied Economics Letters, Taylor & Francis Journals, vol. 14(3), pages 157-161.
    3. George Judge & Laura Schechter, 2009. "Detecting Problems in Survey Data Using Benford’s Law," Journal of Human Resources, University of Wisconsin Press, vol. 44(1).
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