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Distribution of Clump Statistics for a Collection of Words

Part of: Markov processes Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Donald E. K. Martin  and
Deidra A. Coleman
Donald E. K. Martin*
Affiliation:
North Carolina State University
Deidra A. Coleman*
Affiliation:
North Carolina State University
*
∗ Postal address: Department of Statistics, North Carolina State University, 4272 SAS Hall, Raleigh, NC 27695-8203, USA.
∗ Postal address: Department of Statistics, North Carolina State University, 4272 SAS Hall, Raleigh, NC 27695-8203, USA.
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Abstract

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We give an efficient method based on minimal deterministic finite automata for computing the exact distribution of the number of occurrences and coverage of clumps (maximal sets of overlapping words) of a collection of words. In addition, we compute probabilities for the number of h-clumps, word groupings where gaps of a maximal length h between occurrences of words are allowed. The method facilitates the computation of p-values for testing procedures. A word is allowed to contain other words of the collection, making the computation more general, but also more difficult. The underlying sequence is assumed to be Markovian of an arbitrary order.

Keywords

Clumps of a patterncoarsest partitiondeterministic finite automaton

MSC classification

Secondary: 60E05: Distributions 60J05: Discrete-time Markov processes on general state spaces

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 4 , December 2011 , pp. 1049 - 1059
Copyright
Copyright © Applied Probability Trust 2011 

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