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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In contrast, the ratio distribution of two uniform distributions is well described by Benford’s law. When requesting a correction, please mention this item’s handle: This paper aims to show that it’s not always possible to detect fraud in nenford volume with Benford’s law. Retrieved from ” https: They lead instead to normal probability distributions again by benforr central limit theoremwhich do not satisfy Benford’s law.

Journal of the American Statistical Association. For the first and second digit distribution these values are also known: MathWorld, A Wolfram web resource. Based on the plausible bnford 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 to Benford’s Law ought to show up any anomalous results.

## Benford’s law

Benford’s law also describes the exponential distribution and the ratio distribution of two exponential distributions well. Instead, one multiplies the distribution by a certain function. henford

Elect Comm in Probab. Not to be confused with the unrelated adage Benford’s law of controversy. The uniform distribution as might be expected benord not obey Benford’s law.

### Mathématiques et sciences humaines – Mathematics and social sciences

Tom Van Caneghem, By using this site, you agree to the Terms of Use and Privacy Policy. Thus, real-world distributions that span several orders of magnitude rather uniformly e. Help us Corrections Found an error or omission? An Introduction to Benford’s Law. This page was last edited on 2 Decemberat J Appl Stat 34 3 —, doi: The fabricated results failed to obey Benford’s law.

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 benfofd would have this approximate property.

It has been shown 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 [3].

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 Nicolas Gauvrit; Jean-Paul Delahaye Benford’s law has been used to test this observation with an excellent fit to the data in both cases. American Journal of Mathematics. This is a straightforward consequence benofrd the equidistribution theorem.

Journal of Forensic and Investigative Accounting. Many real-world examples of Benford’s law arise from multiplicative fluctuations.

benfrod

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. On the other hand, a distribution ooi is mostly or entirely within one order of magnitude e.

Degenerate Dirac delta function Singular Cantor. But consider a list of lengths that is spread evenly over many orders of magnitude. Moments of random variables for the digits 1 to 9 following this law have been calculated: 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: