Abstract
The distribution of the distance between two (or more) successive occurrences of a specific word in a random sequence of letters is known under different models. In this paper, a more general problem is studied: the distribution of the distance between two (or more) successive occurrences of any word of a given set under a Markov model for the sequence. The generating function and a recurrence for obtaining the probabilities are given. These results are applied to study the distribution of the "CHI" motif in the genome sequence of Haemophilus influenzae.
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Robin, S., Daudin, JJ. Exact Distribution of the Distances between Any Occurrences of a Set of Words. Annals of the Institute of Statistical Mathematics 53, 895–905 (2001). https://doi.org/10.1023/A:1014633825822
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DOI: https://doi.org/10.1023/A:1014633825822