### Santiwipanont, T, Sumetkijakan, S and Wiriyakraikul, T (2019)

#### Benfordness of Chains of Truncated Beta Distributions via a Piecewise Constant Approximation

In: Kreinovich V., Sriboonchitta S. (eds) Structural Changes and their Econometric Modeling. TES 2019. Studies in Computational Intelligence, vol 808. Springer, Cham, pp. 342-351.

**ISSN/ISBN:** Not available at this time.
**DOI:** 10.1007/978-3-030-04263-9_26

**Abstract:** A chain of truncated distributions is constructed from iteratively truncating an initial distribution on the right. We show that if the initial distribution is a piecewise constant approximation of the Beta distribution with parameters 𝛼 and 1 then the mantissas of the chain of truncated distributions converge to a mantissa-limit distribution distinct from the Benford’s law. For general approximating initial distributions, under some suitable conditions on these mantissas, we can conclude that the mantissa-limit distributions converge to the mantissa-limit distribution for the limiting initial distribution. As a result, we obtain an alternative proof of the fact that chains of truncated Beta distributions satisfy Benford’s law in the limit.

**Bibtex:**

```
@InProceedings{,
author="Santiwipanont, Tippawan and Sumetkijakan, Songkiat and Wiriyakraikul, Teerapot",
editor="Kreinovich, Vladik and Sriboonchitta, Songsak",
title="Benfordness of Chains of Truncated Beta Distributions via a Piecewise Constant Approximation",
booktitle="Structural Changes and their Econometric Modeling",
year="2019",
publisher="Springer International Publishing",
address="Cham",
pages="342--351",
isbn="978-3-030-04263-9"
}
```

**Reference Type:** Conference Paper

**Subject Area(s):** Statistics