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

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

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**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 Benfordâ€™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 Benfordâ€™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