On exact and large deviation approximation for the distribution of the longest run in a sequence of two-state Markov dependent trials

DOI10.1239/jap/1053003548zbMath1028.60068OpenAlexW2152104303MaRDI QIDQ4435678

Liqun Wang, James C. Fu, W. Y. Wendy Lou

Publication date: 17 November 2003

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

Full work available at URL: https://doi.org/10.1239/jap/1053003548

zbMATH Keywords

transition probability matrixsuccess runMarkov chain imbeddingprobability of large deviationfailure run

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Large deviations (60F10)

Related Items (22)

A general large deviation principle for longest runs ⋮ Large deviations for longest runs in Markov chains ⋮ Some results associated with the longest run statistic in a sequence of Markov dependent trials ⋮ On longest consecutive patterns in Markov chains ⋮ The \(m\)th longest runs of multivariate random sequences ⋮ Estimating the distribution of one-dimensional discrete scan statistics viewed as extremes of 1-dependent stationary sequences ⋮ On the length of the longest head run ⋮ 1-dependent stationary sequences for some given joint distributions of two consecutive random variables ⋮ Discrete time shock models involving runs ⋮ Exact and asymptotic results for pattern waiting times ⋮ On runs of length exceeding a threshold: normal approximation ⋮ Shortest and longest length of success runs in binary sequences ⋮ ESTIMATOR FOR THE DISTRIBUTION OF THE NUMBERS OF RUNS IN A RANDOM SEQUENCE CONTROLLED BY STATIONARY MARKOV CHAIN ⋮ Distribution of runs in a sequence of exchangeable multi-state trials ⋮ Distribution of the length of the longest common subsequence of two multi-state biological sequences ⋮ A probability model of interregional relations in the context of natural gas supply ⋮ On success runs of length exceeded a threshold ⋮ A test statistic for weighted runs ⋮ Approximating the tail probabilities of the longest run in a sequence of Bernoulli trials ⋮ Approximate probabilities for runs and patterns in i.i.d. and Markov-dependent multistate trials ⋮ Unnamed Item ⋮ Large deviation behavior for the longest head run in an IID Bernoulli sequence

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