# English, Article, Journal or magazine article edition: Regularity of Digits and Significant Digits of Random Variables Theodore P. Hill; Klaus Schürger

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Bookmark: http://trove.nla.gov.au/version/52432
Physical Description
• preprint
Language
• English

### Edition details

Title
• Regularity of Digits and Significant Digits of Random Variables
Author
• Theodore P. Hill
• Klaus Schürger
Physical Description
• preprint
Notes
• 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.
• normal numbers, significant digits, Benford's law, digit-regular random variable, significant-digit-regular random variable, law of least significant digits, floating-point numbers, nonleading digits, trailing digits
• RePEc:bon:bonedp:bgse26_2004
Language
• English
Contributed by
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