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
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Englisch
- Bibliographic citation
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Series: Bonn Econ Discussion Papers ; No. 26/2004
- Classification
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Wirtschaft
- Subject
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normal numbers
significant digits
Benford's law
digit-regular random variable
significant-digit-regular random variable
- Event
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Geistige Schöpfung
- (who)
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Hill, Theodore P.
Schürger, Klaus
- Event
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Veröffentlichung
- (who)
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University of Bonn, Bonn Graduate School of Economics (BGSE)
- (where)
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Bonn
- (when)
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2004
- Handle
- Last update
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10.03.2025, 11:45 AM CET
Data provider
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Object type
- Arbeitspapier
Associated
- Hill, Theodore P.
- Schürger, Klaus
- University of Bonn, Bonn Graduate School of Economics (BGSE)
Time of origin
- 2004