Journal of Applied Probability 55(2), pp. 353-367.

**ISSN/ISBN:** Not available at this time.
**DOI:** 10.1017/jpr.2018.23

- For online information, click here.

**Abstract:** For all α > 0 and real random variables X, we establish sharp bounds for the smallest and the largest deviation of αX from the logarithmic distribution also known as Benford’s law. In the case of uniform X, the value of the smallest possible deviation is determined explicitly. Our elementary calculation puts into perspective the recurring claims that a random variable conforms to Benford’s law, at least approximately, whenever it has large
spread.

**Bibtex:**

```
@article {,
AUTHOR = {Arno Berger and Isaac Twelves},
TITLE = {On the significands of uniform random variables},
JOURNAL = {Journal of Applied Probability},
YEAR = {2018},
VOLUME = {55},
NUMBER = {2},
PAGES = {353-367},
DOI = {10.1017/jpr.2018.23},
}
```

**Reference Type:** Journal Article

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