Journal of Stochastic Processes and their Applications 115(10), pp. 1723-1743.
ISSN/ISBN: 0304-4149 DOI: 10.1016/j.spa.2005.05.003
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^{-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.
Bibtex:
@article {,
AUTHOR = {Hill, Theodore P. and Sch{\"u}rger, Klaus},
TITLE = {Regularity of digits and significant digits of random
variables},
JOURNAL = {Stochastic Process. Appl.},
FJOURNAL = {Stochastic Processes and their Applications},
VOLUME = {115},
YEAR = {2005},
NUMBER = {10},
PAGES = {1723--1743},
ISSN = {0304-4149},
DOI = {10.1016/j.spa.2005.05.003},
URL = {http://dx.doi.org/10.1016/j.spa.2005.05.003},
}
Reference Type: Journal Article
Subject Area(s): Probability Theory