Math. Nachr. 135, 79-83.
ISSN/ISBN: 0025-584X DOI: 10.1002/mana.19881350108
Abstract: Let Y1, Y2, ... be a sequence of random variables and let Mn be the floating-point mantissa of Yn. Further let 1[1,x)(ยท) denote the indicator of the interval [1,x). If Yn/n → Z a.s., where Z≠0 is a further random variable, then the sequence 1[1,x)(Mn) converges a.s. to log x in the sense of H∞-means and logarithmic means, respectively. The speed of convergence in this relations is estimated. As a conclusion, a further argument for Benford's law is provided.
Bibtex:
@article{,
title={On the Almost Sure Convergence of Floating-Point Mantissas and Benford's Law},
author={Schatte, Peter},
journal={Mathematische Nachrichten},
volume={135},
number={1},
pages={79--83},
year={1988},
publisher={Wiley Online Library},
ISSN={0025-584X},
DOI={10.1002/mana.19881350108},
}
Reference Type: Journal Article
Subject Area(s): Analysis, Probability Theory