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• W2317416722 startingPage "851" @default.
• W2317416722 abstract "Consider a sequence of Bernoulli trials with success probability p , and let N n,k denote the number of success runs of length among the first n trials. The Stein–Chen method is employed to obtain a total variation upper bound for the rate of convergence of N n,k to a Poisson random variable under the standard condition np k →λ. This bound is of the same order, O ( p ), as the best known for the case k = 1, i.e. for the classical binomial-Poisson approximation. Analogous results are obtained for occurrences of word patterns, where, depending on the nature of the word, the corresponding rate is at most O ( p k–m ) for some m = 0, 2, ···, k – 1. The technique is adapted for use with two-state Markov chains. Applications to reliability systems and tests for randomness are discussed." @default.
• W2317416722 created "2016-06-24" @default.
• W2317416722 creator A5081970112 @default.
• W2317416722 date "1991-12-01" @default.
• W2317416722 modified "2023-09-24" @default.
• W2317416722 title "Poisson approximations for runs and patterns of rare events" @default.
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• W2317416722 doi "https://doi.org/10.2307/1427680" @default.
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