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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|
|Keywords:||Compound Poisson approximation,Fundamental matrix,Markov sequences,Pattern Correlation Matrices,Polya-Aeppli distribution|
|PDF version:||Click here to retrieve PDF version of paper (226KB)|