On the first k moments of the random count of a pattern in a multi-states sequence generated by a Markov source

Details On the first k moments of the random count of a pattern in a multi-states sequence generated by a Markov source On the first k moments of the random count of a pattern in a multi-states sequence generated by a Markov source

2009-09-22

arxiv.org/abs/0909.4071v1

Journal of Applied Probability, 47(4):1105-1123, 2010

Mathematics

Probability

Scientific paper

10.1239/jap/1294170523

In this paper, we develop an explicit formula allowing to compute the first k moments of the random count of a pattern in a multi-states sequence generated by a Markov source. We derive efficient algorithms allowing to deal both with low or high complexity patterns and either homogeneous or heterogenous Markov models. We then apply these results to the distribution of DNA patterns in genomic sequences where we show that moment-based developments (namely: Edgeworth's expansion and Gram-Charlier type B series) allow to improve the reliability of common asymptotic approximations like Gaussian or Poisson approximations.

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