A new method for obtaining sharp compound Poisson approximation error estimates for sums of locally dependent random variables

DOI10.3150/09-BEJ201zbMath1266.60039arXiv1010.1625OpenAlexW3100253441MaRDI QIDQ453260

Eutichia Vaggelatou, Michael V. Boutsikas

Publication date: 19 September 2012

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.1625

zbMATH Keywords

convergence ratetotal variation distance\(k\)-dependenceideal metricPoisson (compound) approximationsums of independent integer-valued random variables

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50)

Related Items (7)

Compound Poisson approximation ⋮ A new method for bounding the distance between sums of independent integer-valued random variables ⋮ Asymptotically optimal Berry-Esseen-type bounds for distributions with an absolutely continuous part ⋮ The Kolmogorov distance between the binomial and Poisson laws: efficient algorithms and sharp estimates ⋮ Penultimate gamma approximation in the CLT for skewed distributions ⋮ Bounds for the Distance Between the Distributions of Sums of Absolutely Continuous i.i.d. Convex-Ordered Random Variables with Applications ⋮ Poisson approximation of the mixed Poisson distribution with infinitely divisible mixing law

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Compound Poisson process approximation for locally dependent real-valued random variables via a new coupling inequality
• A semigroup approach to Poisson approximation
• A new semigroup technique in Poisson approximation
• Compound Poisson approximation for nonnegative random variables via Stein's method
• Kerstan's method for compound Poisson approximation.
• Estimating Stein's constants for compound Poisson approximation
• Compound Poisson approximation in total variation
• Compound Poisson approximation: A user's guide
• A bound for the distribution of the sum of discrete associated or negatively associated random variables.
• An approximation theorem for the Poisson binomial distribution
• On the distance between convex-ordered random variables, with applications
• Probability Metrics
• Uniform Estimates of the Rate of Convergence in the Multi-Dimensional Central Limit Theorem

This page was built for publication: A new method for obtaining sharp compound Poisson approximation error estimates for sums of locally dependent random variables