Geodesic
Estimate of the Accuracy of the Compound Poisson Approximation for the Distribution of the Number of Matching Patterns
Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 4, pp. 713-723

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Let $X_1,\dots,X_m$ and $Y_1,\dots,Y_n$ be two sequences of independent identically distributed random variables taking on values $1,2,\dots$ . By means of a particular version of the Stein method we construct an estimate of the accuracy of approximation for the distribution of the number of matching patterns of outcomes $X_i,\dots,X_{i+s-1}$ of a given length $s$ in the first sequence with the patterns of outcomes $Y_j,\dots,Y_{j+s-1}$ in the second sequence. The approximating distribution is the distribution of the sum of Poisson number of independent random variables with geometric distribution.
Keywords: long repetitions, coincidence of words, estimates of accuracy of the Poisson approximation, compound Poisson distribution, Stein method, Chen–Stein method. 
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     author = {V. G. Mikhailov},
     title = {Estimate of the {Accuracy} of the {Compound} {Poisson} {Approximation} for the {Distribution} of the {Number} of {Matching} {Patterns}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {713--723},
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     volume = {46},
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     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2001_46_4_a5/}
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V. G. Mikhailov. Estimate of the Accuracy of the Compound Poisson Approximation for the Distribution of the Number of Matching Patterns. Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 4, pp. 713-723. http://geodesic.mathdoc.fr/item/TVP_2001_46_4_a5/