n-digit Benford distributed random variables

Azar Khosravani; Constantin Rasinariu

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arXiv · 1304.8036

n-digit Benford distributed random variables

Azar Khosravani·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 $n$ digits, but it is not guaranteed to have a logarithmic distribution beyond the $n$-th digit. We conclude the paper by giving a general construction method for $n$-digit Benford variables, and provide a concrete example.

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BibTeX RIS

Azar Khosravani, Constantin Rasinariu. 2013-12-20. n-digit Benford distributed random variables. https://arxiv.org/abs/1304.8036

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