Poisson approximation for (k1, k2)-events via the Stein-Chen method

DOI10.1239/jap/1101840553zbMath1062.62025OpenAlexW2087370993MaRDI QIDQ4660532

Palaniappan Vellaisamy

Publication date: 4 April 2005

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1239/jap/1101840553

zbMATH Keywords

rate of convergencebinomial distribution of order \((k_1,k_2)\)Markov-Bernoulli variable

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Probability distributions: general theory (60E05) Approximations to statistical distributions (nonasymptotic) (62E17)

Related Items (18)

Compound Poisson approximation ⋮ On discrete Gibbs measure approximation to runs ⋮ On large deviations for sums of discrete m-dependent random variables ⋮ Approximations related to the sums of \(m\)-dependent random variables ⋮ A compound Poisson convergence theorem for sums of \(m\)-dependent variables ⋮ Distributions of \((k_1,k_2,\dots ,k_m)\)-runs with multi-state trials ⋮ Compound Poisson and signed compound Poisson approximations to the Markov binomial law ⋮ Compound Poisson approximations to sums of extrema of Bernoulli variables ⋮ Distributions associated with \((k_1,k_2)\) events on semi-Markov binary trials ⋮ Lower bound estimates for discrete approximations to sums of weakly dependent random variables ⋮ On Occurrences of F-S Strings in Linearly and Circularly Ordered Binary Sequences ⋮ Nonuniform Approximations for Sums of Discrete m-Dependent Random Variables ⋮ Distributions related to \((k_{1},k_{2})\) events ⋮ Pseudo-binomial approximation to \((k_1, k_2)\)-runs ⋮ Binomial approximation to the Markov binomial distribution ⋮ Poisson type approximations for the Markov binomial distribution ⋮ Infinitely divisible approximations for sums of \(m\)-dependent random variables ⋮ Approximations to weighted sums of random variables

Cites Work

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• Two moments suffice for Poisson approximations: The Chen-Stein method
• Poisson approximations for runs and patterns of rare events
• Dissociated random variables
• Improved Poisson approximations for word patterns
• On discrete distributions of order k
• Successes, runs and longest runs

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