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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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. An Introduction to Benford’s Law. 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.

The total number of observations used in the paper was 20, A number of criteria—applicable particularly to accounting data—have been suggested where Benford’s Law can be expected to apply and not to apply.

Neither the normal distribution nor the ratio distribution of two normal distributions the Cauchy distribution obey Benford’s law.

It is named after physicist Frank Benfordwho stated it in in a paper titled “The Law of Anomalous Numbers”, [4] although it had been previously stated by Simon Newcomb in For instance, the probability that a “2” is encountered as the second digit is [36].

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. Based on the plausible assumption benfrod 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 to Benford’s Law ought to show up any anomalous results.

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Notices of the AMS. Wikimedia Commons has media related to Benford’s law.


There is a generalization of the law to numbers expressed in other bases for example, base 16and also a generalization from leading 1 digit to leading n digits. Statistical fraud detection in campaign finance”. 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.

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. Statistical Mechanics and its ApplicationsElsevier, vol.

As a rule of thumb, the more orders of magnitude that the data evenly covers, the more accurately Benford’s law applies. LaViolette Do dynamical systems follow Benford? 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.

All binary numbers except for 0 start with the digit benvord. Using Benford’s Law to detect fraudulent scientific data. 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. These tests show the inadequacy of our fashion sales time series with the Benford’s Law despite benfoed quality of our data base. Adrien Bonache Karen Moris.

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In terms of conventional probability density referenced to a linear scale rather than log scale, i. Help us Corrections Found an error or omission? 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 benfford prices with a clear trend towards psychological pricing after the nominal shock of the euro introduction.


The ratio of two log normal distributions is a log normal so this distribution was not examined. For example, the height of adult humans almost always starts with a 1 or 2 when measured in meters, and almost always starts with 4, 5, 6, or 7 when measured in feet.

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Benford’s Law and psychological pricing after the euro introduction”. For example, a list of lengths mentioned in scientific papers will include the measurements of bencord, bacteria, plants, and galaxies. Alessandro Gambini; et al. Although the half-normal distribution does not obey Benford’s law, the ratio distribution of two half-normal distributions does.

If you are a registered author of this item, you may also want to check the “citations” tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation. This is a straightforward consequence of the equidistribution theorem. 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.

It is possible to extend the law to digits beyond the first. Lio, some continuous processes satisfy Benford’s Law exactly in the asymptotic limit as the process continues through time.

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.