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Pourquoi la loi de Benford n’est pas mystérieuse

A new general explanation of Bendford’s law
Nicolas Gauvrit and Jean-Paul Delahaye
p. 7-15

Abstracts

According to Benford’s law, the first digit of a random number does not follow a uniform distribution, as many people believe, but a logarithmic distribution. This law was at the begining purely experimental, but it is now established that it holds for various mathematical series and some natural data sets. Concerning data sets, Benford’s law often appears as a good approximation of the reality, but as no more than an approximation.

Our aim is to present a new explanation for this law. We argue that it should not be considered as a mathematical paradox, but as a purely psychological paradox, a result of a cognitive bias. We express a general criterion of regularity on a random variable X and prove that, whenever X follow this criterion, X is approximately Benford.

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References

Bibliographical reference

Nicolas Gauvrit and Jean-Paul Delahaye, “Pourquoi la loi de Benford n’est pas mystérieuse”Mathématiques et sciences humaines, 182 | 2008, 7-15.

Electronic reference

Nicolas Gauvrit and Jean-Paul Delahaye, “Pourquoi la loi de Benford n’est pas mystérieuse”Mathématiques et sciences humaines [Online], 182 | Été 2008, Online since 30 June 2008, connection on 28 September 2021. URL: http://journals.openedition.org/msh/10363; DOI: https://doi.org/10.4000/msh.10363

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About the authors

Nicolas Gauvrit

Equipe didactique des mathématiques (DIDIREM), EA 1547, Centre Chevaleret, Université

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Jean-Paul Delahaye

Laboratoire d’Informatique Fondamentale de Lille (LIFL), UMR USTL/CNRS 8022, Université des sciences et technologie de Lille, bâtiment M3, 59655 Villeneuve d’Ascq Cedex, jeanpaul.delahaye@lifl.fr

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Copyright

© École des hautes études en sciences sociales

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