### Molchanov, S and Wang, X (2004)

#### On the Benford's Empirical Law

Random Operators and Stochastic Equations 12(3), pp. 201-210.

**ISSN/ISBN:** Not available at this time.
**DOI:** 10.1163/1569397042222495

**Abstract:** The paper contains the mathematical analysis of the so-called Benford's Empirical Law, closely related to the famous Weil's theorem about uniform distribution on [0,1] of the sequence of the fractional parts x n = {nα},α is an irrational number, and Poincare theorem about convolutions of the measures on the group S 1 = [0, 1)mod 1. We prove that the Weil's theorem is "robust" in appropriate sense and generalize the Poincare theorem for the class of dependent random variables.

**Bibtex:**

```
@article{,
author = {Molchanov, Stanislav and Wang, Xian},
year = {2004},
month = {09},
pages = {201--210},
title = {On the Benford's Empirical Law},
volume = {12},
number = {3},
journal = {Random Operators and Stochastic Equations},
doi = {10.1163/1569397042222495}
}
```

**Reference Type:** Journal Article

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