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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
Abstract:
Applying the theory of distribution functions of sequences $x_n\in[0,1]$, $n=1,2,…$, 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
DOI:
https://doi.org/10.4213/mzm8848
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English version:
Mathematical Notes, 2010, 88:4, 449–463
Bibliographic databases:
  
UDC:
517
Received: 15.12.2009
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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http://mi.mathnet.ru/eng/mz8848https://doi.org/10.4213/mzm8848 http://mi.mathnet.ru/eng/mz/v88/i4/p485
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