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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Alessandro Gambini; et al.
It has been bennford that this result applies to a wide variety of data sets, including electricity bills, street addresses, stock prices, house prices, population numbers, death rates, lengths of rivers, physical and mathematical constants . Alternate, free web link. This paper aims to show that it’s not always possible to detect fraud in sales volume with Benford’s law.
Détection de fraudes et loi de Benford : quelques risques associés
The fit of the log-normal distribution depends on the mean and the variance of the distribution. If you are a registered author of this benfprd, you may also want to check the “citations” tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
With increasing dfs the fit decreases but much more slowly than the chi square lo. This discovery was later named after Benford making it an example of Stigler’s Law.
However, if one “mixes” numbers from those distributions, for example by taking numbers from newspaper articles, Benford’s law reappears. Official web link subscription required. When requesting a correction, please mention this item’s handle: Nigrini  has suggested the use of a z statistic.
Mathematics > Dynamical Systems
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. Using Benflrd Law to detect fraudulent scientific data. The graph to the right shows Benford’s law for base Corrections All material on this site has been provided by the respective publishers and authors.
His data set included the surface areas of rivers, the sizes of US populations, physical constantsmolecular weightsentries from a mathematical handbook, numbers contained in an issue of Reader’s Digestthe street addresses of the first persons listed in American Men of Science and death rates.
Instead, one multiplies the distribution by a certain function.
Mathématiques et sciences humaines – Mathematics and social sciences
The phenomenon was again noted in by the physicist Frank Benford who tested it on data from 20 different domains and was credited for it.
The general form is:. For instance, the probability that a “2” is encountered as the second digit is . Nicolas Gauvrit; Jean-Paul Delahaye 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.
Neither the right-truncated normal distribution nor the ratio distribution of two right-truncated normal distributions are well described by Benford’s law. MathWorld, A Wolfram web resource. Benford’s law also describes the exponential distribution and the ratio distribution of two exponential distributions well.
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. Thus, real-world distributions that span several orders of magnitude rather uniformly e.
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.
The authors describe this argument, but say it “still leaves open the question of why it is reasonable to assume that the logarithm of the spread, as opposed to the spread itself—or, say, the log log spread—should be large. Adrien Bonache Karen Moris. If the digits were distributed uniformly, they would each occur about It lki named after physicist Frank Benfordwho stated it in in a paper bnford “The Law of Anomalous Numbers”,  although it had been previously stated by Simon Newcomb in See, for example, .
Benford’s law has been used to test this observation with an excellent fit to the data in both cases.
Benford’s Law has been invoked as evidence of fraud in the Iranian elections and also used to analyze other election results. This method of testing with application to Benford’s law is described in Ostrovski I use video games hardwares sales volume, in Benfodr from aprilin United-States, France, Germany and United-Kigngdom from november Other distributions that have been examined include the Muth distributionGompertz distributionWeibull distributiongamma distributionlog-logistic distribution and the exponential power distribution all of which show reasonable agreement with the law.
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The reason is that the logarithm of the stock price is undergoing a random walkso over time its probability distribution will get more and more broad and smooth see above. 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.
Based on the plausible assumption that people who make up figures tend to distribute their digits fairly uniformly, a simple comparison of first-digit frequency distribution from the data with the expected distribution according lii Benford’s Law ought to show up any anomalous results.
Benford’s law is sometimes stated in a stronger form, asserting that the fractional part of the logarithm of data is typically close to uniformly distributed between 0 and 1; from this, the main claim about the distribution of first digits can be derived.