Risque associé à l’utilisation de la loi de Benford pour détecter les fraudes dans le secteur de la mode [Risk of Reviews based on Benford Law in the Fashion. Français: Fréquences relatives d’apparition de la 1ère décimale d’un résultat de mesure selon la Loi de Benford Licence: Date, 31 March A Simple Explanation of Benford’s Law. R. M. FEWSTER. Benford’s Law, also known as the first-digit law, has long been seen as a tantalizing and mysterious.

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Détection de fraudes et loi de Benford : quelques risques associés

The phenomenon was again noted in by the physicist Frank Benford[4] who tested it on data from 20 different domains and was credited for it. Journal of the American Statistical Association. From Wikipedia, benfordd free encyclopedia. On the other hand, a distribution that is mostly or entirely within one order of magnitude e.

If there is a list of lengths, the distribution of first digits of numbers in the list may be generally similar regardless of whether all the lengths are expressed in metres, ,oi yards, or feet, or inches, etc.

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An empirical investigation and a novel explanation”. This allows to link your profile to this item. Square roots and reciprocals do not obey this law. See, for example, [1]. Benford Bernoulli beta-binomial binomial categorical hypergeometric Poisson binomial Rademacher soliton discrete uniform Zipf Zipf—Mandelbrot.

Official web link subscription required. Moments of random variables for the digits 1 to 9 following this law have been calculated: Therefore, this is the distribution expected if the mantissae of the logarithms of the numbers but not the numbers themselves are uniformly and randomly distributed.

This is not surprising as this distribution is weighted towards larger numbers. This is a straightforward consequence of the equidistribution theorem. When requesting a correction, please mention this item’s handle: Examining a list of the heights of the 60 tallest structures in the world by category shows that 1 is by far the most common leading digit, irrespective of the unit of measurement cf.


Many real-world examples of Benford’s law arise from multiplicative fluctuations. The introduction of the euro inwith its various exchange rates, distorted existing nominal price patterns while at the same time retaining real prices. This method of testing with application to Benford’s law is described in Ostrovski The law states that in many naturally occurring collections of numbers, the leading significant digit is likely to be small. Views Read Edit View history.

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If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. After a short review of litterature and an introduction of my method, I test the adequation with Benford’s law of my 56 weekly sales volume time series with benord statistics.

American Journal of Mathematics. A table of the exact probabilities for the joint occurrence of the first two digits according to Benford’s law is available, [48] as is the population correlation between the first and second digits: Alternate, free web link.

Help us Corrections Found an error or omission? The Kolmogorov—Smirnov test and henford Kuiper test are more powerful when the sample size is small particularly when Li corrective factor is used. On the other hand, for the right distribution, the ratio of the areas of red and blue is very different from the ratio of the widths of each red and blue bar.

The variance has a much greater effect on the fit than does the mean. To be sure of approximate agreement with Benford’s Law, the distribution has to be approximately invariant when scaled up by any factor up to 10; a lognormally distributed data set with wide dispersion would have this approximate property. Thus, real-world distributions that span several orders of magnitude rather uniformly e. A narrow probability distribution of the log of a variable, shown on a log scale [11].


Not to be confused with the unrelated adage Benford’s law of controversy.

The fabricated results failed to obey Benford’s law. You can help correct errors and omissions. General contact details of provider: The Newcomb-Benford law in its relation to some common distributions.

Détection de fraudes et loi de Benford : quelques risques associés – Munich Personal RePEc Archive

Notices of the AMS. Like other general principles about natural data — for example the fact that many data sets are well bneford by a normal distribution — there are illustrative examples and explanations that cover many of the cases where Benford’s law applies, though there are many other cases where Benford’s law applies that resist a simple explanation.

Larger values of both parameters result in better agreement with the law. Formann provided an alternative explanation by directing attention to the interrelation between the distribution of the significant digits and the distribution of the observed variable. Benford’s law was empirically tested against the numbers up to the 10th digit generated by a number of important distributions, including the uniform distributionthe exponential distributionthe half-normal distributionthe right-truncated normalthe normal distributionthe chi square distribution and the log normal distribution.

Benford’s law

Discrete Ewens multinomial Dirichlet-multinomial negative multinomial Continuous Dirichlet generalized Dirichlet multivariate Laplace multivariate normal multivariate stable multivariate t normal-inverse-gamma normal-gamma Matrix-valued inverse matrix gamma inverse-Wishart matrix normal matrix t matrix gamma normal-inverse-Wishart normal-Wishart Wishart. Nigrini [33] has koi the use of a z statistic. In other projects Wikimedia Commons.