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- W4253502484 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.
- W4253502484 created "2022-05-12" @default.
- W4253502484 creator A5081970112 @default.
- W4253502484 date "1991-12-01" @default.
- W4253502484 modified "2023-10-13" @default.
- W4253502484 title "Poisson approximations for runs and patterns of rare events" @default.
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- W4253502484 doi "https://doi.org/10.1017/s0001867800023983" @default.
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