Improved compound Poisson approximation for the number of occurrences of any rare word family in a stationary Markov chain - INRAE - Institut national de recherche pour l’agriculture, l’alimentation et l’environnement Access content directly
Journal Articles Advances in Applied Probability Year : 2007

Improved compound Poisson approximation for the number of occurrences of any rare word family in a stationary Markov chain

Abstract

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

Dates and versions

hal-02663611 , version 1 (31-05-2020)

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Etienne Roquain, Sophie S. Schbath. Improved compound Poisson approximation for the number of occurrences of any rare word family in a stationary Markov chain. Advances in Applied Probability, 2007, 39 (1), pp.128-140. ⟨10.1239/aap/1175266472⟩. ⟨hal-02663611⟩

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