Arbeitspapier

Regularity of Digits and Significant Digits of Random Variables

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.

Language
Englisch

Bibliographic citation
Series: Bonn Econ Discussion Papers ; No. 26/2004

Classification
Wirtschaft
Subject
normal numbers
significant digits
Benford's law
digit-regular random variable
significant-digit-regular random variable

Event
Geistige Schöpfung
(who)
Hill, Theodore P.
Schürger, Klaus
Event
Veröffentlichung
(who)
University of Bonn, Bonn Graduate School of Economics (BGSE)
(where)
Bonn
(when)
2004

Handle
Last update
10.03.2025, 11:45 AM CET

Data provider

This object is provided by:
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.

Object type

  • Arbeitspapier

Associated

  • Hill, Theodore P.
  • Schürger, Klaus
  • University of Bonn, Bonn Graduate School of Economics (BGSE)

Time of origin

  • 2004

Other Objects (12)