# 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.
122 Citations

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## References

SHOWING 1-10 OF 10 REFERENCES

### A Statistical Derivation of the Significant-Digit Law

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.

• Mathematics
• 2000
In Chapter 8 we discussed additive models (AM) of the form $$E(Y|X) = c + \sum\limits_{\alpha = 1}^d {g_\alpha (x_\alpha )} .$$ (1) Note that we put EY = c and E(g α (X α ) = 0 for

### Cubic Splines for Estimating the Distribution of Residence Time Using Individual Resightings Data

• Mathematics
• 2009
Residence time, or stopover duration, is of considerable interest to biologists studying migratory populations. We present a method for estimating the distribution of residence time for a population

### Breaking the (Benford) Law: Statistical Fraud Detection in Campaign Finance,’

• The American Statistician,
• 2007

• 2000

### The Law of Anomalous Numbers,’

• Proceedings of the American Philosophical Society,
• 1938

• 2007

• 2007