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Publication Citation: Joint Distribution of Pattern Frequencies and Multivariate Polya-Aeppli Law

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Author(s): Andrew L. Rukhin;
Title: Joint Distribution of Pattern Frequencies and Multivariate Polya-Aeppli Law
Published: January 14, 2010
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
Pages: 15 pp.
Keywords: Compound Poisson approximation;Fundamental matrix;Markov sequences;Pattern Correlation Matrices;Polya-Aeppli distribution
Research Areas: Statistics
PDF version: PDF Document Click here to retrieve PDF version of paper (226KB)