The mathematics of Benford’s law: a primer

@article{Berger2020TheMO,
  title={The mathematics of Benford’s law: a primer},
  author={Arno Berger and Theodore P. Hill},
  journal={Statistical Methods \& Applications},
  year={2020},
  pages={1-17}
}
  • A. Berger, T. Hill
  • Published 17 September 2019
  • Mathematics
  • Statistical Methods & Applications
This article provides a concise overview of the main mathematical theory of Benford’s law in a form accessible to scientists and students who have had first courses in calculus and probability. In particular, one of the main objectives here is to aid researchers who are interested in applying Benford’s law, and need to understand general principles clarifying when to expect the appearance of Benford’s law in real-life data and when not to expect it. A second main target audience is students of… 
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References

SHOWING 1-10 OF 12 REFERENCES
An Introduction to Benford's Law
Random distribution functions
How cani oine choose, at ranidom, a probability measture oni the Ullit interval? This paper develops the answer anniiounced in [4]. Section 1, w-hich can be skipped without logical loss, gives a…
Benford’s Law: Applications for Forensic Accounting
  • Auditing, and Fraud Detection. John Wiley & Sons, Hoboken, NJ
  • 2012
The law of anomalous numbers
  • Proc. Amer. Philosophical Soc., 78(4):551– 572
  • 1938
On the significands of uniform random variables
TLDR
This elementary calculation puts into perspective the recurring claims that a random variable conforms to Benford's law, at least approximately, whenever it has large spread.
A Statistical Derivation of the Significant-Digit Law
TLDR
If distributions are selected at random (in any "unbi- ased" way) and random samples are then taken from each of these dis- tributions, the significant digits of the combined sample will converge to the logarithmic (Benford) distribution.
Benford's law : applications for forensic accounting, auditing, and fraud detection
A powerful new tool for all forensic accountants, or anyone who analyzes data that may have been altered Benford's Law gives the expected patterns of the digits in the numbers in tabulated data such…
Benford's Law: Theory and Applications
TLDR
Emphasizing common challenges and techniques across the disciplines, this accessible book shows how Benford’s law can serve as a productive meeting ground for researchers and practitioners in diverse fields.
Note on the Frequency of Use of the Different Digits in Natural Numbers
Benford’s Law Strikes Back: No Simple Explanation in Sight for Mathematical Gem
TLDR
The claim by Feller and subsequent authors that ‘‘regularity and large spread implies Benford’s Law’’ is fallacious for any reasonable definitions of regularity and spread (measure of dispersion).
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