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February, 1977 The Distribution of Leading Digits and Uniform Distribution Mod 1
Persi Diaconis
Ann. Probab. 5(1): 72-81 (February, 1977). DOI: 10.1214/aop/1176995891


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.


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Persi Diaconis. "The Distribution of Leading Digits and Uniform Distribution Mod 1." Ann. Probab. 5 (1) 72 - 81, February, 1977.


Published: February, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0364.10025
MathSciNet: MR422186
Digital Object Identifier: 10.1214/aop/1176995891

Primary: 10K05
Secondary: 60F05

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

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 1 • February, 1977
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