POWER LAWS IN PREFERENTIAL ATTACHMENT GRAPHS AND STEIN'S METHOD FOR THE NEGATIVE BINOMIAL DISTRIBUTION

被引：11

作者：

Ross, Nathan ^{[1
]}

机构：

[1] Univ Calif Berkeley, Berkeley, CA 94720 USA

来源：

ADVANCES IN APPLIED PROBABILITY | 2013年 / 45卷 / 03期

关键词：

Stein's method; negative binomial distribution; random graph; preferential attachment; distributional transformation; power law; BOUNDS; RATES;

D O I：

10.1017/S0001867800006625

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：

For a family of linear preferential attachment graphs, we provide rates of convergence for the total variation distance between the degree of a randomly chosen vertex and an appropriate power law distribution as the number of vertices tends to infinity. Our proof uses a new formulation of Stein's method for the negative binomial distribution, which stems from a distributional transformation that has the negative binomial distributions as the only fixed points.

引用

页码：876 / 893

页数：18

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