Mathematical Social Sciences, Volume 71, September 2014, pp. 1–5.

**ISSN/ISBN:** Not available at this time.
**DOI:** 10.1016/j.mathsocsci.2014.03.006

- For online information, click here.
- For additional online information, click here.

**Abstract:** If X is uniformly distributed modulo 1 and Y is independent of X then Y+X is also uniformly distributed modulo 1. We prove a converse for any continuous random variable Y (or a reasonable approximation to a continuous random variable) so that if X and Y+X are equally distributed modulo 1 and Y is independent of X then X is uniformly distributed modulo 1 (or approximates the uniform distribution equally reasonably). This translates into a characterization of Benford’s law through a generalization of scale-invariance: from multiplication by a constant to multiplication by an independent random variable.

**Bibtex:**

```
@article {,
AUTHOR = {Wojcik, MMichal Ryszard},
TITLE = {A characterization of Benford’s law through generalized scale-invariance},
JOURNAL = {Mathematical Social Sciences},
YEAR = {2014},
VOLUME = {71},
PAGES = {1--5},
MONTH = {September},
DOI = {10.1016/j.mathsocsci.2014.03.006},
}
```

**Reference Type:** Journal Article

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