| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 972573 | Mathematical Social Sciences | 2014 | 5 Pages |
•We characterize Benford’s law through generalized scale-invariance.•Multiplication by a constant is replaced with multiplication by a random variable.•Continuous and discrete random variables are considered.
If XX is uniformly distributed modulo 1 and YY is independent of XX then Y+XY+X is also uniformly distributed modulo 1. We prove a converse for any continuous random variable YY (or a reasonable approximation to a continuous random variable) so that if XX and Y+XY+X are equally distributed modulo 1 and YY is independent of XX then XX 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.
