https://github.com/argentini/argentini.benford

Experiment with Benford's Law to find data anomalies in number lists and images (Windows, macOS, Linux, .NET 8.0, x64, Arm64, Apple Silicon)
https://github.com/argentini/argentini.benford

analytics anomalous-numbers benfords-law dotnet fake fraud normal-distribution numbers patterns

Last synced: 7 months ago
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Experiment with Benford's Law to find data anomalies in number lists and images (Windows, macOS, Linux, .NET 8.0, x64, Arm64, Apple Silicon)

• Host: GitHub
• URL: https://github.com/argentini/argentini.benford
• Owner: argentini
• License: mit
• Created: 2022-05-27T15:03:27.000Z (over 3 years ago)
• Default Branch: main
• Last Pushed: 2024-09-03T15:38:42.000Z (about 1 year ago)
• Last Synced: 2025-04-01T22:46:51.944Z (8 months ago)
• Topics: analytics, anomalous-numbers, benfords-law, dotnet, fake, fraud, normal-distribution, numbers, patterns
• Language: C#
• Homepage: https://nonsequiturs.com/
• Size: 1.85 MB
• Stars: 8
• Watchers: 2
• Forks: 2
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • Contributing: CONTRIBUTING.md
  • License: LICENSE
  • Code of conduct: CODE_OF_CONDUCT.md

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README

          
# What is Benford’s Law?

We all know about the [Normal distribution](https://en.wikipedia.org/wiki/Normal_distribution) and its ubiquity in all kind of natural phenomena or observations. But there is another law of numbers which does not get much attention but pops up everywhere — from nations’ population to stock market volumes to the domain of universal physical constants.

**Benford’s Law**, also known as the **Law of First Digits**, the **Phenomenon of Significant Digits**, or the **Law of Anomalous Numbers** is the finding that the first digits (or numerals to be exact) of the numbers found in series of records of the most varied sources do not display a uniform distribution, but rather are arranged in such a way that the digit “1” is the most frequent, followed by “2”, “3”, and so in a successively decreasing manner down to “9”.

The distribution of first digits should follow the pattern in the image below:

![Benford's Law Chart](https://upload.wikimedia.org/wikipedia/commons/thumb/4/46/Rozklad_benforda.svg/440px-Rozklad_benforda.svg.png)

This distribution is specifically:

```

Digit   Benford [%]

=====   ===========

1       30.10

2       17.61

3       12.49

4       09.69

5       07.92

6       06.69

7       05.80

8       05.12

9       04.58

```

## Project

This project is a .NET console app project to play with Benford's Law on images and a text file with numeric values. You can fill the text file with a large, random data set from most any source to see if the data follows this law and if not, implying the data has been artificially altered. Likewise you can put a set of images (*.jpg, *.tiff) into the *images* folder to analyze the pixel values in them. If the image results deviate from the law it could mean the image has been processed or altered.