### Scott, PD and Fasli, M (2001)

#### Benford’s law: an empirical investigation and a novel explanation

CSM Technical Report 349, Department of Computer Science, University of Essex, UK.

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

**Abstract:** This report describes an investigation into Benford’s Law for the distribution
of leading digits in real data sets. A large number of such data sets have been
examined and it was found that only a small fraction of them conform to the
law. Three classes of mathematical model of processes that might account for
such a leading digit distribution have also been investigated. We found that
based on the notion of taking the product of many random factors the most
credible. This led to the identification of a class of lognormal distributions,
those whose shape parameter exceeds 1, which satisfy Benford’s Law. This in
turn led us to a novel explanation for the law: that it is fundamentally a
consequence of the fact that many physical quantities cannot meaningfully take
negative values. This enabled us to develop a simple set of rules for
determining whether a given data set is likely to conform to Benford’s Law.
Our explanation has an important advantage over previous attempts to account
for the law: it also explains which data sets will not have logarithmically
distributed leading digits. Some techniques for generating data that satisfy
Benford’s law are described and the report concludes with a summary and a
discussion of the practical implications.

**Bibtex:**

```
@techreport{,
title={Benford’s law: An empirical investigation and a novel explanation},
author={Scott, Paul and Fasli, Maria},
type=CSM Technical Report 349},
year={2001},
institution={Department of Computer Science, University of Essex, UK],
}
```

**Reference Type:** E-Print

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