The Annals of Probability

The Distribution of Leading Digits and Uniform Distribution Mod 1

Persi Diaconis

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Abstract

The lead digit behavior of a large class of arithmetic sequences is determined by using results from the theory of uniform distribution $\operatorname{mod} 1$. Theory for triangular arrays is developed and applied to binomial coefficients. A conjecture of Benford's that the distribution of digits in all places tends to be nearly uniform is verified.

Article information

Source
Ann. Probab., Volume 5, Number 1 (1977), 72-81.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995891

Digital Object Identifier
doi:10.1214/aop/1176995891

Mathematical Reviews number (MathSciNet)
MR422186

Zentralblatt MATH identifier
0364.10025

JSTOR
links.jstor.org

Subjects
Primary: 10K05
Secondary: 60F05: Central limit and other weak theorems

Keywords
Lead digits uniform distribution mod 1 probabilistic number theory Stein's method for dependent variables

Citation

Diaconis, Persi. The Distribution of Leading Digits and Uniform Distribution Mod 1. Ann. Probab. 5 (1977), no. 1, 72--81. doi:10.1214/aop/1176995891. https://projecteuclid.org/euclid.aop/1176995891


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