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### 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