On a relationship between Uspensky's theorem and Poisson approximations
type: Item
instance of: scholarly article
title: On a relationship between Uspensky's theorem and Poisson approximations
zbMATH Open document ID: 0675.60027
DOI: 10.1007/BF00049425
author: P. Deheuvels
author: Dietmar Pfeifer
published in: Annals of the Institute of Statistical Mathematics
publication date: 1988-01-01T00:00:00Z
review text: The authors show that a result of \textit{J. V. Uspensky} [Ann. Math., II. Ser. 32, 306-312 (1931; Zbl 0002.20004)] for the Poisson approximation of the distribution of sums of independent Bernoulli random variables can be rewritten in terms of the Poisson convolution semigroup. This can be used in turn to derive bounds on the deviation of the distribution of sums of independent Bernoulli random variables from an appropriate Poisson distribution under various types of probability metrics. Results obtained generalize the work of \textit{S. Ya. Shorgin} [Teor. Veroyatn. Primen. 22, 867-871 (1977; Zbl 0392.60021); English translation in Theory Probab. Appl. 22, 846-850 (1978)]. Sharpness of Poisson versus normal approximations is compared.
Mathematics Subject Classification ID: 60F99
zbMATH DE Number: 4105959
zbMATH Keywords: Poisson convolution semigroup
zbMATH Keywords: Sharpness of Poisson versus normal approximations
reviewed by: B. L. S. Prakasa Rao
MaRDI profile type: Publication
cites work: Asymptotic expansions in the Poisson limit theorem
cites work: On the rate of Poisson convergence
cites work: The normal approximation to the Poisson distribution and a proof of a conjecture of Ramanujan
cites work: A semigroup approach to Poisson approximation
cites work: Operator semigroups and Poisson convergence in selected metrics
cites work: An approximation theorem for the Poisson binomial distribution
cites work: A semigroup-theoretic proof of Poisson's limit law
cites work: A semigroup setting for distance measures in connexion with Poisson approximation
cites work: Some Elementary Results on Poisson Approximation in a Sequence of Bernoulli Trials
cites work: Approximation of a Generalized Binomial Distribution
cites work: Probability Metrics
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description: scientific article; zbMATH DE number 4105959