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Joint Distribution of Pattern Frequencies and Multivariate Polya-Aeppli Law



Andrew L. Rukhin


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.
Theory of Probability and Its Applications


Compound Poisson approximation, Fundamental matrix, Markov sequences, Pattern Correlation Matrices, Polya-Aeppli distribution


Rukhin, A. (2010), Joint Distribution of Pattern Frequencies and Multivariate Polya-Aeppli Law, Theory of Probability and Its Applications, [online], (Accessed July 13, 2024)


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Created January 14, 2010, Updated February 19, 2017