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Improved compound Poisson approximation for the number of occurrences of any rare word family in a stationary markov chain
Published online by Cambridge University Press: 01 July 2016
Abstract
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We derive a new compound Poisson distribution with explicit parameters to approximate the number of overlapping occurrences of any set of words in a Markovian sequence. Using the Chen-Stein method, we provide a bound for the approximation error. This error converges to 0 under the rare event condition, even for overlapping families, which improves previous results. As a consequence, we also propose Poisson approximations for the declumped count and the number of competing renewals.
MSC classification
Secondary:
60C05: Combinatorial probability
- Type
- General Applied Probability
- Information
- Copyright
- Copyright © Applied Probability Trust 2007
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