Useful inequalities for the longest run distribution

DOI10.1016/S0167-7152(99)00108-XzbMath0961.60071MaRDI QIDQ1970812

Marco Muselli

Publication date: 21 March 2000

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

zbMATH Keywords

Stein's methodcompound Poisson approximationBernoulli trialslongest success run

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10)

Related Items (8)

Some results associated with the longest run statistic in a sequence of Markov dependent trials ⋮ On longest consecutive patterns in Markov chains ⋮ Success runs in a sequence of exchangeable binary trials ⋮ The \(m\)th longest runs of multivariate random sequences ⋮ Limiting behaviors for longest consecutive switches in an IID Bernoulli sequence ⋮ A nonparametric lack-of-fit test for heteroscedastic regression models ⋮ On runs of length exceeding a threshold: normal approximation ⋮ On success runs of length exceeded a threshold

Cites Work

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• Poisson approximation for dependent trials
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• Exact Reliability Formulas for Linear & Circular Consecutive-k-out-of-n:F Systems
• Simplified Reliabilities for Consecutive-k-out-of-nSystems
• On Reliability of a Large Consecutive-k-out-of-n:F System with (k - 1)-step Markov Dependence
• Distribution Theory of Runs: A Markov Chain Approach
• Longest run of consecutive observations having a specified attribute

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