Template-Type: ReDIF-Paper 1.0
Title: Regularity of Digits and Significant Digits of Random Variables
Author-Name: Theodore P. Hill
Author-Name: Klaus Schürger
Author-Email: 
Classification-JEL: 
Keywords: 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 
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. 
Note: 
Length: 26
Creation-Date: 2004-11	
Revision-Date: 
File-URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonedp/bgse26_2004.pdf
File-Format: application/pdf
Handle: RePEc:bon:bonedp:bgse26_2004