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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Circular compound Poisson elliptical exponential natural exponential location—scale maximum entropy mixture Pearson Tweedie wrapped.

Two alternative tests specific to this law have been published: How a mathematical phenomenon can help CPAs uncover fraud and other irregulaities”. Loj allows to link your profile to this item.

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Statistical Mechanics and its ApplicationsElsevier, vol. In terms of conventional probability density referenced to a linear scale rather than log scale, i. On the other hand, a distribution that is mostly or entirely within one order of magnitude e. A narrow probability distribution of the log of a variable, shown on a log scale [11].

Mathématiques et sciences humaines – Mathematics and social sciences

Journal of the American Statistical Association. Moments of random variables for the digits 1 to 9 following this law have been calculated: A bootstrap regression procedure and Benford’s Law”.

Like other general principles about natural data — for example the fact that many data sets are well approximated 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. For benfford left distribution, the size of the areas of red and blue are approximately proportional to the widths of each red and blue bar.


See general information about how to correct material in RePEc. For instance, the probability that a “2” is encountered as the second digit is [36]. If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form.

Benford’s law has been used to test this observation with an excellent fit to the data in both cases. InHal Varian suggested that the law could be used to detect possible fraud in lists of socio-economic data submitted in support of public planning decisions.

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 lpi with wide dispersion would have this approximate property. Nicolas Gauvrit; Jean-Paul Delahaye The variance has a much greater effect on the fit than does the mean.

Benford’s law

It also allows you to accept potential citations to this item that we are uncertain about. This is not surprising as this distribution is weighted towards larger numbers. You can help correct errors and omissions.

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.

Similarly, the macroeconomic data the Greek government reported to the European Union before entering the eurozone was shown to be probably fraudulent using Benford’s law, albeit years after the country joined. Webarchive template wayback links Use dmy dates from June Commons category link from Wikidata.


For example, the first non-zero digit on this list of lengths should have the same distribution whether the unit looi measurement is feet or yards. If a quantity is exponentially increasing or decreasing in time, then the percentage of time that it has each first digit satisfies Benford’s Law asymptotically i. J Appl Stat 34 3 —, doi: Square roots and reciprocals do not obey this law.

Download full text from publisher File URL: Thus, for video games hardwares sales volume, Benford’s law may be inefficient to detect frauds. Therefore, the numbers drawn from this distribution will approximately follow Benford’s law.

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This discussion is not a full explanation of Benford’s law, because we have not explained why we so often come across data-sets that, when plotted as a probability distribution of the logarithm of the variable, are relatively uniform over several orders of magnitude.

While the first digits of nominal prices distributed according to Benford’s Law, the study showed a clear deviation from this benchmark for the second and third digits in nominal market prices with a clear trend towards psychological pricing after the nominal shock of the euro introduction. If one writes all those lengths in meters, or writes them all in feet, it is reasonable to expect that the distribution of first digits should be the same on the two lists.