On a relationship between Uspensky's theorem and Poisson approximations

DOI10.1007/BF00049425zbMath0675.60027MaRDI QIDQ1122213

Dietmar Pfeifer, Paul Deheuvels

Publication date: 1988

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

zbMATH Keywords

Poisson convolution semigroupSharpness of Poisson versus normal approximations

Mathematics Subject Classification ID

Limit theorems in probability theory (60F99)

Related Items (22)

Improvements in the Poisson approximation of mixed Poisson distributions ⋮ A semigroup approach to Poisson approximation with respect to the point metric ⋮ Poisson approximations in selected metrics by coupling and semigroup methods with applications ⋮ Pseudo-Poisson approximation for Markov chains ⋮ On using the first difference in the Stein-Chen method ⋮ Compound Poisson approximations for symmetric vectors ⋮ Compound Poisson approximations for sums of 1-dependent random variables. II ⋮ Compound Poisson approximations for sums of 1-dependent random variables. I ⋮ A Charlier-Parseval approach to Poisson approximation and its applications ⋮ In praise (and search) of J. V. Uspensky ⋮ Compound Poisson and signed compound Poisson approximations to the Markov binomial law ⋮ Note on nonuniform estimate for compound Poisson approximations to \(2\)-runs ⋮ Limit Theorems for Record Indicators in Threshold $F^\alpha$-Schemes ⋮ On moderate deviations in Poisson approximation ⋮ Large deviations by Poisson approximations ⋮ Two-parametric compound binomial approximations. ⋮ Sharp constants in the Poisson approximation ⋮ Binomial approximation to the Markov binomial distribution ⋮ Poisson type approximations for the Markov binomial distribution ⋮ Convergence Rate Estimates in the Global CLT for Compound Mixed Poisson Distributions ⋮ Poisson approximation ⋮ On the Poisson approximation for some multinomial distributions

Cites Work

• A semigroup setting for distance measures in connexion with Poisson approximation
• A semigroup approach to Poisson approximation
• Operator semigroups and Poisson convergence in selected metrics
• Asymptotic expansions in the Poisson limit theorem
• A semigroup-theoretic proof of Poisson's limit law
• An approximation theorem for the Poisson binomial distribution
• Probability Metrics
• On the rate of Poisson convergence
• Some Elementary Results on Poisson Approximation in a Sequence of Bernoulli Trials
• Approximation of a Generalized Binomial Distribution
• The normal approximation to the Poisson distribution and a proof of a conjecture of Ramanujan

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