Please use this identifier to cite or link to this item:
Hill, Theodore P.
Schürger, Klaus
Year of Publication: 
Series/Report no.: 
Bonn econ discussion papers 2004,26
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.
normal numbers
significant digits
Benford's law
digit-regular random variable
significant-digit-regular random variable
Document Type: 
Working Paper

Files in This Item:

Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.