Advances and Applications in Statistics
Volume 36, Issue 2, Pages 119 - 130
(October 2013)
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n-DIGIT BENFORD DISTRIBUTED RANDOM VARIABLES
Azar Khosravani and Constantin Rasinariu
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Abstract: The scope of this paper is twofold. First, to emphasize the use of the mod 1 map in exploring the digit distribution of random variables. We show that the well-known base- and scale-invariance of Benford variables are consequences of their associated mod 1 density functions being uniformly distributed. Second, to introduce a new concept of the n-digit Benford variable. Such a variable is Benford in the first ndigits, but it is not guaranteed to have a logarithmic distribution beyond the nth digit. We conclude the paper by giving a general construction method for n-digit Benford variables, and provide a concrete example. |
Keywords and phrases: Benford’s law, random variables, mod 1 map, scale-invariance, base- invariance. |
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