Poisson approximations of multinomial distributions and point processes

DOI10.1016/0047-259X(88)90153-4zbMath0651.60060MaRDI QIDQ1106546

Paul Deheuvels, Dietmar Pfeifer

Publication date: 1988

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

total variation distanceoperator treatment of Poisson approximations

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Semigroups (20M99)

Related Items (15)

Multivariate Poisson and Poisson process approximations with applications to Bernoulli sums and -statistics ⋮ Kac's representation from an asymptotic viewpoint ⋮ Approximation of the generalized Poisson binomial distribution: Asymptotic expansions ⋮ Compound Poisson approximations for symmetric vectors ⋮ Poisson approximation of empirical processes ⋮ Refined total variation bounds in the multivariate and compound Poisson approximation ⋮ On the optimality of multivariate Poisson approximation ⋮ Poisson approximation ⋮ On the rate of multivariate Poisson convergence ⋮ Probabilities of large deviations for the \(\chi^2\) approximation ⋮ Asymptotic expansions for generalized Poisson measures ⋮ Asymptotic estimation of the parameters of multivariate point processes. ⋮ On the stability of splitting difference schemes with respect to boundary conditions ⋮ Approximation of a sample by a Poisson point process ⋮ On the Poisson approximation for some multinomial distributions

Cites Work

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• Some Poisson approximations using compensators
• A semigroup approach to Poisson approximation
• Operator semigroups and Poisson convergence in selected metrics
• Partitions of point processes: Multivariate Poisson approximations
• The Poisson approximation for dependent events
• A general Poisson approximation theorem
• An approximation theorem for the Poisson binomial distribution
• The Poisson Theorem and Markov Chains
• Approximation of Binomial Distributions by Infinitely Divisible Ones
• Weak and Strong Convergence of the Distributions of Counting Processes
• On the rate of Poisson convergence
• A general poisson approximation theorem
• Asymptotic Behavior of the Multinomial Dstribution

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