### Kulikova, AA, Prokhorov, YV and Khokhlov, VI (2006)

#### H.F.D. (H-function Distribution) and Benford's Law. I

Theory of Probability & Its Applications 50(2), pp. 311-315 .

**ISSN/ISBN:** Not available at this time.
**DOI:** 10.1137/S0040585X97981706

**Abstract:** This paper notes a connection among a wide class of the so-called HF-random variables, approximately uniform distributions, and Benford's law. This connection is considered in detail with the help of examples of random variables having gamma-distribution. Let Y be a random variable having gamma-distribution with parameter $\alpha$. It is proved that the distribution of a fractional part of the logarithm of Y with respect to any base larger than 1 converges to the uniform distribution on the interval [0,1] for $\alpha$ to 0. This implies that the probability distribution of the first significant digit of Y for small $\alpha$ can be approximately described by Benford's law. The order of the approximation is illustrated by tables.
Read More: https://epubs.siam.org/doi/10.1137/S0040585X97981706

**Bibtex:**

```
@article{,
author = {Kulikova, A. and Prokhorov, Y. and Khokhlov, V.},
title = {H.F.D. (H-function Distribution) and Benford's Law. I},
journal = {Theory of Probability \& Its Applications},
volume = {50},
number = {2},
pages = {311--315},
year = {2006},
doi = {10.1137/S0040585X97981706},
URL = {https://doi.org/10.1137/S0040585X97981706},
eprint = {https://doi.org/10.1137/S0040585X97981706},
}
```

**Reference Type:** Journal Article

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