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Exact distribution of word counts in shuffled sequences

Part of: Distribution theory Combinatorics Combinatorial probability Markov processes

Published online by Cambridge University Press:  01 July 2016

Einar Andreas Rødland
Einar Andreas Rødland*
Affiliation:
Rikshospitalet–Radiumhospitalet HF, University of Oslo
*
∗ Postal address: Institute of Medical Microbiology, Centre for Molecular Biology and Neuroscience, University of Oslo, Rikshospitalet–Radiumhospitalet HF, N-0027 Oslo, Norway. Email address: [email protected]
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Abstract

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In DNA sequences, specific words may take on biological functions as marker or signalling sequences. These may often be identified by frequent-word analyses as being particularly abundant. Accurate statistics is needed to assess the statistical significance of these word frequencies. The set of shuffled sequences - letter sequences having the same k-word composition, for some choice of k, as the sequence being analysed - is considered the most appropriate sample space for analysing word counts. However, little is known about these word counts. Here we present exact formulae for word counts in shuffled sequences.

Keywords

Sequence shufflingMarkov chainword countexact distributionhypergeometric distributiongeneralised hypergeometric seriesmoment generating functiongenome sequence analysisdirected graphEuler path

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 05A15: Exact enumeration problems, generating functions 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) 62E15: Exact distribution theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 38 , Issue 1 , March 2006 , pp. 116 - 133
Copyright
Copyright © Applied Probability Trust 2006 

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