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Matematicheskie Zametki, 2010, Volume 88, Issue 4, Pages 485–501
DOI: https://doi.org/10.4213/mzm8848 (Mi mzm8848) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Benford's Law and Distribution Functions of Sequences in $(0,1)$

V. Baláža, K. Nagasakab, O. Strauchc

a Slovak University of Technology, Bratislava, Slovakia
b Hosei University, Tokyo, Japan
c Mathematical Institute, Slovak Academy of Sciences, Bratislava, Slovakia
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DOI: https://doi.org/10.4213/mzm8848
Abstract: Applying the theory of distribution functions of sequences $x_n\in[0,1]$, $n=1,2,\dots$, we find a functional equation for distribution functions of a sequence $x_n$ and show that the satisfaction of this functional equation for a sequence $x_n$ is equivalent to the fact that the sequence $x_n$ to satisfies the strong Benford law. Examples of distribution functions of sequences satisfying the functional equation are given with an application to the strong Benford law in different bases. Several direct consequences from uniform distribution theory are shown for the strong Benford law.
Keywords: distribution function of a sequence, Benford's law, density of occurrence of digits.
Received: 15.12.2009
English version:
Mathematical Notes, 2010, Volume 88, Issue 4, Pages 449–463
DOI: https://doi.org/10.1134/S0001434610090178
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: V. Baláž, K. Nagasaka, O. Strauch, “Benford's Law and Distribution Functions of Sequences in $(0,1)$”, Mat. Zametki, 88:4 (2010), 485–501; Math. Notes, 88:4 (2010), 449–463
Citation in format AMSBIB
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\paper Benford's Law and Distribution Functions of Sequences in $(0,1)$
\jour Mat. Zametki
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\issue 4
\pages 485--501
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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