### Balanzario, EP and Sánchez-Ortiz, J (2010)

#### Sufficient conditions for Benford’s law

Statistics & Probability Letters 80(23-24), pp. 1713-1719.

**ISSN/ISBN:** Not available at this time.
**DOI:** 10.1016/j.spl.2010.07.014

**Abstract:** We present two sufficient conditions for an absolutely continuous random variable to obey Benford’s law for the distribution of the first significant digit. These two sufficient conditions suggest that Benford’s law will not often be observed in everyday sets of numerical data. On the other hand, we recall that there are two processes by way of which a random variable can come close to following Benford’s law. The first of these is the multiplication of independent random variables and the second is the exponentiation of a random variable to a large power. Our working tool is the Poisson sum formula of Fourier analysis. Like the central limit theorem, Benford’s law has an asymptotic nature.

**Bibtex:**

```
@article{,
title = "Sufficient conditions for Benford's law",
journal = "Statistics & Probability Letters",
volume = "80",
number = "23",
pages = "1713--1719",
year = "2010",
issn = "0167-7152",
doi = "https://doi.org/10.1016/j.spl.2010.07.014",
url = "http://www.sciencedirect.com/science/article/pii/S0167715210002087",
author = "Eugenio P. Balanzario and Jorge Sanchez-Ortiz",
}
```

**Reference Type:** Journal Article

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