Maxwell Consulting Archives, http://www.maxwell-consulting.com/Benford_Logarithmic_Transformation.pdf. Last retrieved 10 September 2014.

**ISSN/ISBN:** Not available at this time.
**DOI:** Not available at this time.

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**Abstract:** We review the history and description of Benford’s Law - the observation that many naturally occurring numerical data collections exhibit a logarithmic distribution of digits. By creating numerous hypothetical examples, we identify several cases that satisfy Benford’s Law and several that do not. Building on prior work, we create and demonstrate a “Benford Test” to determine from the functional form of a probability density function whether the resulting distribution of digits will find close agreement with Benford’s Law. We also discover that one may generalize the first-digit distribution algorithm to include non-logarithmic transformations. This generalization shows that Benford’s Law rests on the tendency of the transformed and shifted data to exhibit a uniform distribution.

**Bibtex:**

```
@misc{,
AUTHOR = {Pimbley, Joseph M.},
TITLE = {Benford’s Law as a Logarithmic Transformation},
ORGANIZATION = {Maxwell Consulting},
YEAR = {2014},
URL = {http://www.maxwell-consulting.com/Benford_Logarithmic_Transformation.pdf},
NOTE={Last retrieved 10 September 2014},
}
```

**Reference Type:** E-Print

**Subject Area(s):** General Interest