Poisson approximation for random sums of Bernoulli random variables

DOI10.1016/0167-7152(91)90135-EzbMath0728.60051MaRDI QIDQ805064

Nikos Yannaros

Publication date: 1991

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

zbMATH Keywords

rates of convergencepoint processesrandom number of Bernoulli summandstotal variation distance between the distribution

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (12)

Improvements in the Poisson approximation of mixed Poisson distributions ⋮ Poisson Approximations for Sum of Bernoulli Random Variables and its Application to Ewens Sampling Formula ⋮ Stochastic spikes and Poisson approximation of one-dimensional stochastic differential equations with applications to continuously measured quantum systems ⋮ Convergence rates for the degree distribution in a dynamic network model ⋮ Unnamed Item ⋮ On Poisson approximations for the Ewens sampling formula when the mutation parameter grows with the sample size ⋮ Poisson approximation for (k₁, k₂)-events via the Stein-Chen method ⋮ On success runs of a fixed length in Bernoulli sequences: exact and asymptotic results ⋮ Some results on approximation for distributions of random sums by Poisson distribution ⋮ Poisson approximation of multivariate Poisson mixtures ⋮ On compound Poisson approximation for sums of random variables ⋮ Poisson approximation

Cites Work

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• The Poisson approximation for dependent events
• A general Poisson approximation theorem
• On the rate of Poisson convergence
• A note on the upper bound for the distance in total variation between the binomal and the Poisson distribution

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