Search for a tool
Benford's Law

Tool to verify the Benford's law. Test digital data whether they are random or not and if numbers follow Benford's law. This test is used in particular for the detection of fraud, such as accounting or finance.

Results

Benford's Law -

Tag(s) : Mathematics,Fun,Data processing

dCode and you

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day!
You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? Contact-me!


Team dCode read all messages and answer them if you leave an email (not published). It is thanks to you that dCode has the best Benford's Law tool. Thank you.

This page is using the new English version of dCode, please make comments !

Benford's Law

Sponsored ads

Digital Data Analyzer



Also on dCode: Frequency Analysis

Tool to verify the Benford's law. Test digital data whether they are random or not and if numbers follow Benford's law. This test is used in particular for the detection of fraud, such as accounting or finance.

Answers to Questions

What is the definition of the Benford's Law?

Benford's law states that in the majority of natural collections of numbers (ie. lists of numbers derived from reality and not created artificially), the first significant digit is usually small. This law applies very well to numbers representing orders of magnitude: prices, populations, lengths, etc.

The digit 0 is excluded because it is not significant. The law therefore applies to numbers between 1 and 9.

Mathematically we can describe the probability that a digit is the first significant digit of a number in a collection of numbers by the formula:

$$ P(d)=\log_{10} \left(1+\frac{1}{d}\right) $$

The corresponding percentageshref are:

10.30120.17630.125
40.09750.07960.067
70.05880.05190.046

How to test a dataset with Benford's Law?

dCode uses the Chi2 test (χ²). Just enter the data in the text box, dCode will calculate the frequency of occurrence of the first significant digits.

dCode considers that the data are correlated with the distribution of Benford's law, when the p-value is less than 0.05 (95% test).

What kind of data generally obeys to Benford's law?

Data obeying the Benford law :

- The numbers resulting from transactions, accounting data: turnover, refunds, sales, etc.

- Results of addition, multiplicationhref or exponentiationhref

- Fibonacci numbershref, powers, factorialshref, etc.

What kind of data does not obey to Benford's law?

Data not obeying the Benford law:

- Sequential numbers: street numbers, invoices, etc.

- Significant numbers, ie. numbers that contents is defined by a nomenclature (for example: card number), or whose value is defined by human thinking (for example: a price of $ 9.99)

- Numbers coming from a collection limited by a minimum or a maximum or another criterion that can introduce a statistical bias.

Ask a new question

Source code

dCode retains ownership of the source code of the script Benford's Law. Except explicit open source licence (free / freeware), any algorithm, applet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any snippet or function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in PHP (or Java, C#, Python, Javascript, etc.) which dCode owns rights can be transferred after sales quote. So if you need to download the Benford's Law script for offline use, for you, your company or association, see you on contact page !

Questions / Comments


Team dCode read all messages and answer them if you leave an email (not published). It is thanks to you that dCode has the best Benford's Law tool. Thank you.


Source : http://www.dcode.fr/benford-law
© 2016 dCode — The ultimate 'toolkit' website to solve every problem. dCode