### Lee, J, Cho, WKT and Judge, GG (2009)

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

CUDARE Working Papers, Dept. of Agricultural and Resource Economics, UC Berkeley.

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

**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:**

```
@techreport{,
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},
institution = {Dept. of Agricultural and Resource Economics, UC Berkeley},
year={2009},
url = {https://escholarship.org/uc/item/9745m98d},
}
```

**Reference Type:** Technical Report

**Subject Area(s):** Probability Theory, Statistics