A Simple Explanation of Benford's Law

@article{Fewster2009ASE,
  title={A Simple Explanation of Benford's Law},
  author={Rachel M. Fewster},
  journal={The American Statistician},
  year={2009},
  volume={63},
  pages={26 - 32}
}
  • R. Fewster
  • Published 1 February 2009
  • Education
  • The American Statistician
Benfords Law occurs is, however, elusive. Many researchers have verified for themselves that the law is widely obeyed, but have also noted that the popular explanations are not completely satisfying. In this article we do nothing rigorous, but provide a simple, intuitive explanation of why and when the law applies. It is intended that the explanation should be accessible to school students and anyone with a basic knowledge of probability density curves and logarithms. 
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117 Citations
Highly Influential Citations
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Background Citations
57
Methods Citations
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Results Citations
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117 Citations

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Feller's classic text 'An Introduction to Probability Theory and its Applications' contains a derivation of the well known significant-digit law called Benford's law. More specifically, Feller gives…
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TLDR
In two studies, some empirical support for the generalized Benford analysis is provided and it is concluded that familiarity with the numerical domain involved as well as cognitive effort only have a mild effect on the method’s accuracy.
Playing with Benford's Law
This paper presents a classroom experiment, the simulations, and a research which familiarize the students with the Benford’s Law. This law is widely used in a tax fraud detecting procedures. This…
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It is shown that the distribution of first digits of real world observations would not be uniform, but instead follow a trend where measurements with lower first digit occur more frequently than those with higher first digits.
A derivation of Benford's Law ... and a vindication of Newcomb
We show how Benford's Law (BL) for first, second, ..., digits, emerges from the distribution of digits of numbers of the type $a^{R}$, with $a$ any real positive number and $R$ a set of real numbers…
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It is suggested that Benford's law does not depend on properties linked with the log function, and two theorems are proved, making up a formal version of this intuition: scattered and regular r.v.'s do approximately follow Benford't law.
A basic theory of Benford's Law ∗
Drawing from a large, diverse body of work, this survey presents a comprehensive and unified introduction to the mathematics underlying the prevalent logarithmic distribution of significant digits…
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