 Regularity of Digits and Significant Digits of Random VariablesTheodore P. Hill and Klaus Schürger No 26/2004, Bonn Econ Discussion Papers from University of Bonn, Bonn Graduate School of Economics (BGSE) Abstract: A random variable X is digit-regular (respectively, significant-digit-regular) if the probability that every block of k given consecutive digits (significant digits) appears in the b-adic expansion of X approaches b &supk; as the block moves to the right, for all integers b > 1 and k ? 1. Necessary and sufficient conditions are established, in terms of convergence of Fourier coefficients, and in terms of convergence in distribution modulo 1, for a random variable to be digit-regular (significant-digit regular), and basic relationships between digit-regularity and various classical classes of probability measures and normal numbers are given. These results provide a theoretical basis for analyses of roundoff errors in numerical algorithms which use floating-point arithmetic, and for detection of fraud in numerical data via using goodness-of-fit of the least significant digits to uniform, complementing recent tests for leading significant digits based on Benford's law. Keywords: normal numbers; significant digits; Benford's law; digit-regular random variable; significant-digit-regular random variable (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:zbw:bonedp:262004 Access Statistics for this paper More papers in Bonn Econ Discussion Papers from University of Bonn, Bonn Graduate School of Economics (BGSE) Contact information at EDIRC. |
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