Skip to main content

benfordslaw is to test if an empirical (observed) distribution differs significantly from a theoretical (expected, Benfords) distribution.

Project description


Python PyPI Version License Coffee Github Forks GitHub Open Issues Project Status Downloads Downloads Open In Colab

  • benfordslaw is Python package to test if an empirical (observed) distribution differs significantly from a theoretical (expected, Benfords) distribution. The law states that in many naturally occurring collections of numbers, the leading significant digit is likely to be small. This method can be used if you want to test whether your set of numbers may be artificial (or manipulated). If a certain set of values follows Benford's Law then model's for the corresponding predicted values should also follow Benford's Law. Normal data (Unmanipulated) does trend with Benford's Law, whereas Manipulated or fraudulent data does not.

  • Assumptions of the data:

    1. The numbers need to be random and not assigned, with no imposed minimums or maximums.
    2. The numbers should cover several orders of magnitude
    3. Dataset should preferably cover at least 1000 samples. Though Benford's law has been shown to hold true for datasets containing as few as 50 numbers.


  • Install benfordslaw from PyPI (recommended). benfordslaw is compatible with Python 3.6+ and runs on Linux, MacOS X and Windows.
  • It is distributed under the MIT license.


pip install benfordslaw
  • Alternatively, install benfordslaw from the GitHub source:
git clone
cd benfordslaw
pip install -U .

Import benfordslaw package

from benfordslaw import benfordslaw

# Initialize
bl = benfordslaw(alpha=0.05)

# Load elections example
df = bl.import_example(data='USA')

# Extract election information.
X = df['votes'].loc[df['candidate']=='Donald Trump'].values

# Print
# array([ 5387, 23618,  1710, ...,    16,    21,     0], dtype=int64)

# Make fit
results =

# Plot
bl.plot(title='Donald Trump')


Please cite benfordslaw in your publications if this is useful for your research. Here is an example BibTeX entry:

  author={Erdogan Taskesen},



  • Erdogan Taskesen, github: erdogant
  • This work is created and maintained in my free time. If you wish to buy me a Coffee for this work, it is very appreciated.
  • Contributions are welcome.
  • Star it if you like it!

Project details

Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Files for benfordslaw, version 1.0.2
Filename, size File type Python version Upload date Hashes
Filename, size benfordslaw-1.0.2-py3-none-any.whl (9.2 kB) File type Wheel Python version py3 Upload date Hashes View
Filename, size benfordslaw-1.0.2.tar.gz (7.3 kB) File type Source Python version None Upload date Hashes View

Supported by

AWS AWS Cloud computing Datadog Datadog Monitoring DigiCert DigiCert EV certificate Facebook / Instagram Facebook / Instagram PSF Sponsor Fastly Fastly CDN Google Google Object Storage and Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Salesforce Salesforce PSF Sponsor Sentry Sentry Error logging StatusPage StatusPage Status page