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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
