Rukhin, A.
(2010),
Joint Distribution of Pattern Frequencies and Multivariate Polya-Aeppli Law, Theory of Probability and Its Applications, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=50909
(Accessed April 3, 2025)
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Joint Distribution of Pattern Frequencies and Multivariate Polya-Aeppli Law
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Abstract
This paper studies the joint distribution of frequencies of several overlapping words in a Markov sequence. Usually, characteristics of this distribution are expressed in terms of so-called pattern correlation matrix. A more direct approach allows for explicit formulas which involve the fundamental matrix of the Markov chain whose states are patterns of a given length. this form leads to the probability generating function of the asymptotic joint distribution of pattern frequencies.Citation
Theory of Probability and Its Applications
Volume
54
Pub Type
Journals
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Keywords
Compound Poisson approximation, Fundamental matrix, Markov sequences, Pattern Correlation Matrices, Polya-Aeppli distribution
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Created January 14, 2010, Updated February 19, 2017