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December, 1957 Exact Markov Probabilities from Oriented Linear Graphs
Reed Dawson, I. J. Good
Ann. Math. Statist. 28(4): 946-956 (December, 1957). DOI: 10.1214/aoms/1177706795


Using a theorem due to de Bruijn, van Aardenne-Ehrenfest, C. A. B. Smith and Tutte concerning the number of circuits in oriented linear graphs, an expression is found for the probability of a specified frequency count of $m$-tuples in a circular sequence where the $n$-tuple $(n < m)$ count is given. The corresponding result for linear sequences can be deduced--see [14]. The result is valid for stationary Markovity of any order up to and including the $(n - 1)$-st. A method of deriving asymptotic distributions is indicated, and a few additional observations made concerning the distribution of pairs in a circular array.


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Reed Dawson. I. J. Good. "Exact Markov Probabilities from Oriented Linear Graphs." Ann. Math. Statist. 28 (4) 946 - 956, December, 1957.


Published: December, 1957
First available in Project Euclid: 27 April 2007

zbMATH: 0078.31701
MathSciNet: MR93819
Digital Object Identifier: 10.1214/aoms/1177706795

Rights: Copyright © 1957 Institute of Mathematical Statistics

Vol.28 • No. 4 • December, 1957
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