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Schatte, P (1988)

On the Almost Sure Convergence of Floating-Point Mantissas and Benford Law

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)() 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.

@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