Poisson approximation

DOI10.1214/18-PS318zbMath1422.60028arXiv1901.01847OpenAlexW4246882069MaRDI QIDQ2323908

Serguei Novak

Publication date: 13 September 2019

Published in: Probability Surveys (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.01847

zbMATH Keywords

asymptotic expansionsPoisson approximationcompound Poisson approximationtotal variation distancePoisson process approximationaccuracy of approximationlong head runslong match patterns

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Asymptotic distribution theory in statistics (62E20) Inequalities; stochastic orderings (60E15) Central limit and other weak theorems (60F05) Extreme value theory; extremal stochastic processes (60G70) Sums of independent random variables; random walks (60G50) Approximations to statistical distributions (nonasymptotic) (62E17) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items

Multivariate Poisson and Poisson process approximations with applications to Bernoulli sums and -statistics ⋮ Criteria for Poisson process convergence with applications to inhomogeneous Poisson-Voronoi tessellations ⋮ Poisson approximation. Addendum ⋮ Compound Poisson approximation ⋮ Extremal Probability Bounds in Combinatorial Optimization ⋮ On the \(T\)-test ⋮ On the rate of Poisson approximation to Bernoulli partial sum processes ⋮ Compound Poisson approximations in \(\ell_p\)-norm for sums of weakly dependent vectors ⋮ The Poisson binomial distribution -- old \& new ⋮ Monotonicity properties of the Poisson approximation to the binomial distribution ⋮ Poisson approximation in terms of the Gini-Kantorovich distance ⋮ Poisson approximation with applications to stochastic geometry ⋮ On the accuracy of approximation of the binomial distribution by the Poisson law

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