Open Access
2014 Distribution of the sum-of-digits function of random integers: A survey
Louis H. Y. Chen, Hsien-Kuei Hwang, Vytas Zacharovas
Probab. Surveys 11: 177-236 (2014). DOI: 10.1214/12-PS213


We review some probabilistic properties of the sum-of-digits function of random integers. New asymptotic approximations to the total variation distance and its refinements are also derived. Four different approaches are used: a classical probability approach, Stein’s method, an analytic approach and a new approach based on Krawtchouk polynomials and the Parseval identity. We also extend the study to a simple, general numeration system for which similar approximation theorems are derived.


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Louis H. Y. Chen. Hsien-Kuei Hwang. Vytas Zacharovas. "Distribution of the sum-of-digits function of random integers: A survey." Probab. Surveys 11 177 - 236, 2014.


Published: 2014
First available in Project Euclid: 10 October 2014

zbMATH: 1327.60029
MathSciNet: MR3269227
Digital Object Identifier: 10.1214/12-PS213

Primary: 60C05 , 60F05
Secondary: 11K16 , 11N37 , 62E17

Keywords: asymptotic normality , digital sums , Gray codes , Krawtchouk polynomials , numeration systems , Stein’s method , sum-of-digits function , total variation distance

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.11 • 2014
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