The exact distribution of the k-tuple statistic for sequence homology

W. Y. Wendy Lou

Statistics & Probability Letters, 2003, vol. 61, issue 1, 51-59

Abstract: The distribution theory of runs and patterns has become increasingly useful in the field of biological sequence homology. One important application in detecting tandem duplications among DNA sequence segments is the k-tuple statistic Sn,k, the sum of matches in matching-runs of length k or longer in a sequence of n i.i.d. Bernoulli trials with success/matching probability p. Current approaches to this distribution problem are based on various approximations, due mainly to the numerical complexity of computing the exact distribution using a straightforward combinatorial approach. In this paper, we obtain a simple and efficient expression for the exact distribution of Sn,k using the principle of finite Markov chain imbedding. Our numerical results illustrate most importantly that for pattern lengths in the range n=10 to 100, a range commonly used in detecting DNA tandem repeats, the distribution, in general, is highly skewed and far from normal.

Keywords: DNA; sequence; matching; Markov; chain; Runs; and; patterns (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (10)

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