### Wiriyakraikul, T, Sumetkijakan,S and Santiwipanont,T (2017)

#### Benford’s law for chains of truncated distribution

In: Proceedings of the 22nd Annual Meeting in Mathematics (AMM 2017), Chiang Mai University, Chiang Mai, 2–4 June.

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

**Abstract:** It is quite prevalent that the first digits of real world data are distributed approximately according to a discrete logarithmic distribution proposed and studied by Benford, hence the name Benford’s law. Given an initial distribution F = F1, we study a sequence of random variables Xn’s, or equivalently distributions Fn’s, for which Xn+1 is distributed according to F, right-truncated by Xn. The sequence is called the chain of truncated distributions generated by F . We show that if F is supported on [0, k], k > 0 and uniformly distributed on a neighborhood of 0 then the chain of truncated distributions generated by F satisfies Benford’s law in the limit.

**Bibtex:**

```
@inproceedings{,
AUTHOR={Teerapot Wiriyakraikul and Tippawan Santiwipanont,and Songkiat Sumetkijakan},
TITLE={Benford’s law for chains of truncated distribution},
BOOKTITLE={Proceedings of the 22nd Annual Meeting in Mathematics (AMM 2017)},
ADDRESS={Chiang Mai University, Chiang Mai},
MONTH={June2--4},
YEAR={2017},
URL={http://www.math.science.cmu.ac.th/amm2017/proceedings/PRO-03.pdf},
}
```

**Reference Type:** Conference Paper

**Subject Area(s):** Applied Mathematics, Probability Theory, Statistics