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.
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/
@article{TVP_2001_46_4_a5,
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},
year = {2001},
volume = {46},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2001_46_4_a5/}
}
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