Distribution of the sum-of-digits function of random integers: A survey

被引：11

作者：

Chen, Louis H. Y. ^{[1
]}

Hwang, Hsien-Kuei ^{[2
,4
]}

Zacharovas, Vytas ^{[3
,5
]}

机构：

[1] Natl Univ Singapore, Dept Math, 10 Lower Kent Ridge Rd, Singapore 119076, Singapore

[2] Acad Sinica, Inst Informat Sci, Inst Stat Sci, Taipei 115, Taiwan

[3] Vilnius Univ, Dept Math & Informat, Vilnius, Lithuania

[4] Natl Univ Singapore, Inst Math Sci, Singapore, Singapore

[5] Acad Sinica, Inst Stat Sci, Taipei, Taiwan

来源：

PROBABILITY SURVEYS | 2014年 / 11卷

关键词：

Sum-of-digits function; Stein's method; Gray codes; total variation distance; numeration systems; Krawtchouk polynomials; digital sums; asymptotic normality;

D O I：

10.1214/12-PS213

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：177 / 236

页数：60

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