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.
Publié le : 1977-02-14
Classification:
Lead digits,
uniform distribution mod 1,
probabilistic number theory,
Stein's method for dependent variables,
10K05,
60F05
@article{1176995891,
author = {Diaconis, Persi},
title = {The Distribution of Leading Digits and Uniform Distribution Mod 1},
journal = {Ann. Probab.},
volume = {5},
number = {6},
year = {1977},
pages = { 72-81},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995891}
}
Diaconis, Persi. The Distribution of Leading Digits and Uniform Distribution Mod 1. Ann. Probab., Tome 5 (1977) no. 6, pp. 72-81. http://gdmltest.u-ga.fr/item/1176995891/