A compound Poisson process approximation for the number of occurrences of multiple words in a sequence of letters is derived, where the letters are assumed to be independent and identically distributed. Using the Chen-Stein method, a bound on the error in the approximation is provided. For rare words, this error tends to zero as the length of the sequence increases to infinity. As an application the efficiency of the approximation for the number of occurrences of rare stemloop motifs in DNA sequences is illustrated.
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