Poisson approximations of multinomial distributions and point processes
type: Item
instance of: scholarly article
title: Poisson approximations of multinomial distributions and point processes
zbMATH Open document ID: 0651.60060
DOI: 10.1016/0047-259X(88)90153-4
author: P. Deheuvels
author: Dietmar Pfeifer
published in: Journal of Multivariate Analysis
publication date: 1988-01-01T00:00:00Z
review text: The authors extend their operator treatment of Poisson approximations of sums of independent Bernoulli random variables [Ann. Probab. 14, 663-676 (1986; Zbl 0597.60019)] to the setting of multivariate Bernoulli summands. If the summands are identically distributed, the distance estimates follow from the univariate case [by an observation of Michel, ASTIN Bull. (1987)]. In general, a leading term estimate for the total variation distance is obtained, together with an error estimate which, however, is not yet ideal in the case equivalent, in the univariate setting, to \(\sum_{i}p^ 2_ i\to \infty\).
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 20M99
zbMATH DE Number: 4062283
zbMATH Keywords: operator treatment of Poisson approximations
zbMATH Keywords: total variation distance
reviewed by: A. D. Barbour
MaRDI profile type: Publication
cites work: Asymptotic Behavior of the Multinomial Dstribution
cites work: On the rate of Poisson convergence
cites work: Q3956153
cites work: Some Poisson approximations using compensators
cites work: A semigroup approach to Poisson approximation
cites work: Operator semigroups and Poisson convergence in selected metrics
cites work: Q3025927
cites work: The Poisson approximation for dependent events
cites work: Q4043971
cites work: Weak and Strong Convergence of the Distributions of Counting Processes
cites work: Q4114580
cites work: An approximation theorem for the Poisson binomial distribution
cites work: Q3769675
cites work: Approximation of Binomial Distributions by Infinitely Divisible Ones
cites work: A general Poisson approximation theorem
cites work: Partitions of point processes: Multivariate Poisson approximations
cites work: The Poisson Theorem and Markov Chains
cites work: A general poisson approximation theorem
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description: scientific article; zbMATH DE number 4062283