### Lee, J, Cho, WKT and Judge, G (2010)

#### Stigler’s approach to recovering the distribution of first significant digits in natural data sets

Statistics and Probability Letters 80(2), pp. 82-88.

**ISSN/ISBN:** Not available at this time.
**DOI:** 10.1016/j.spl.2009.09.015

**Abstract:** In 1881, Newcomb conjectured that the first significant digits (FSDs) of
numbers in statistical tables would follow a logarithmic distribution with the
digit “1” occurring most often. However, because Newcomb’s proposal was not
presented with a theoretical basis, it was not given much attention. Fifty-seven
years later, Benford argued for the same principle and showed it was relevant
to a large range of data sets, and the logarithmic FSD distribution became
known as “Benford’s Law.” In the mid-1940s, Stigler claimed Benford’s Law
contained a theoretical inconsistency and supplied an alternative derivation for
the distribution of FSDs. In this paper, we examine the theoretical basis of the
Stigler distribution and extend his reasoning by incorporating FSD first moment
information and information-theoretic methods.

**Bibtex:**

```
@article{,
title={Stigler’s approach to recovering the distribution of first significant digits in natural data sets},
author={Lee, Joanne and Cho, Wendy K Tam and Judge, George G},
journal={Statistics \& Probability Letters},
volume={80},
number={2},
pages={82--88},
year={2010},
publisher={Elsevier},
DOI={doi:10.1016/j.spl.2009.09.015},
}
```

**Reference Type:** Journal Article

**Subject Area(s):** Statistics