Resource title

Regularity of Digits and Significant Digits of Random Variables

Resource image

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Resource description

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?k 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.

Resource author

Theodore P. Hill, Klaus Schürger

Resource publisher

Resource publish date

Resource language

eng

Resource content type

text/html

Resource resource URL

http://hdl.handle.net/10419/22903

Resource license

Adapt according to the presented license agreement and reference the original author.