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Kanemitsu, S, Nagasaka, K, Rauzy, G and Shiue, JS (1988)

On Benford’s law: the first digit problem

Lecture Notes in Mathematics 1299, pp. 158-169 (eds. Watanabe, S, and Prokhorov, YV).

ISSN/ISBN: 978-3-540-18814-8 DOI: 10.1007/BFb0078471

Abstract: Our standpoint in this paper is based, on the one hand, on B.J. Flehinger's philosophy that since the smallest population containing the set of significant figures of all possible physical constants must be the set N of all positive integers, one should look for the explanation of Benford's law in the properties of N as represented in the radix number system; and, on the other hand on Johann Cigler's heuristic observation that if for a sequence an of positive reals, (log an) is uniformly distributed mod 1 then (an) may be said to satisfy Benford's law in the strictest sense, the sense of natural density. Thus we adopt ℕ as a model of the population and determine whether Benford's law holds or not for the integer sequences sampled according to certain sampling procedures.

@incollection{, title={On Benford's law: The first digit problem}, author={Kanemitsu, Shigeru and Nagasaka, Kenji and Rauzy, G{\'e}rard and Shiue, Jau-Shyong}, booktitle={Probability Theory and Mathematical Statistics}, pages={158--169}, year={1988}, publisher={Springer}, DOI={10.1007/BFb0078471}, ISBN={978-3-540-18814-8}, }

Reference Type: Book Chapter

Subject Area(s): Analysis, Number Theory