Total variation error bounds for geometric approximation

DOI10.3150/11-BEJ406zbMath1412.60012arXiv1005.2774MaRDI QIDQ1952436

Erol A. Peköz, Nathan Ross, Adrian Roellin

Publication date: 30 May 2013

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.2774

zbMATH Keywords

Stein's methodgeometric distributionpreferential attachment modelYaglom's theoremdiscrete equilibrium distribution

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Approximations to statistical distributions (nonasymptotic) (62E17) Convergence of probability measures (60B10) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Renewal theory (60K05)

Related Items (12)

Binomial approximation for sum of indicators with dependent neighborhoods ⋮ Convergence rates for the degree distribution in a dynamic network model ⋮ Degree asymptotics with rates for preferential attachment random graphs ⋮ Pólya urns with immigration at random times ⋮ Generalized gamma approximation with rates for urns, walks and trees ⋮ Stein's method for the single server queue in heavy traffic ⋮ Wasserstein and Kolmogorov error bounds for variance-gamma approximation via Stein's method. I ⋮ Fluctuations in a general preferential attachment model via Stein's method ⋮ Convergence Rate of Random Geometric Sum Distributions to the Laplace Law ⋮ Joint degree distributions of preferential attachment random graphs ⋮ Power Laws in Preferential Attachment Graphs and Stein's Method for the Negative Binomial Distribution ⋮ New error bounds for Laplace approximationviaStein’s method

Cites Work

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• The first divisible sum
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• Total variation asymptotics for sums of independent integer random variables
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• The degree sequence of a scale-free random graph process
• Stein's Method for Compound Geometric Approximation
• Normal Approximation by Stein’s Method
• Multivariate normal approximations by Stein's method and size bias couplings

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