Khosravani, Azar; Rasinariu, Constantin \(n\)-digit benford distributed random variables. (English) Zbl 1286.11114 Adv. Appl. Stat. 36, No. 2, 119-130 (2013). Summary: 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. Cited in 1 Document MSC: 11K06 General theory of distribution modulo \(1\) 11K36 Well-distributed sequences and other variations 60E05 Probability distributions: general theory Keywords:Benford’s law; random variables; mod 1 map; scale-invariance; base-invariance PDFBibTeX XMLCite \textit{A. Khosravani} and \textit{C. Rasinariu}, Adv. Appl. Stat. 36, No. 2, 119--130 (2013; Zbl 1286.11114) Full Text: arXiv Link