Martina, Donald E. K. and Aston, John A. D.. (2008) Waiting time distribution of generalized later patterns. Computational Statistics & Data Analysis, Volume 52 (Number 11). pp. 4879-4890. ISSN 0167-9473

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Abstract

In this paper the concept of later waiting time distributions for patterns in multi-state trials is generalized to cover a collection of compound patterns. that must all be counted pattern-specific numbers of times, and a practical method is given to compute the generalized distribution. The solution given applies to overlapping counting and two types of non-overlapping counting, and the underlying sequences are assumed to be Markovian of a general order. Patterns are allowed to be weighted so that an occurrence is counted multiple times, and patterns may be completely included in longer patterns. Probabilities are computed through an auxiliary Markov chain. As the state space associated with the auxiliary chain can be quite large if its setup is handled in a naive fashion, an algorithm is given for generating a "minimal". state space that leaves out states that can never be reached. For the case of overlapping counting, a formula that relates probabilities for intersections of events to probabilities for unions of subsets of the events is also used, so that the distribution is also computed in terms of probabilities for competing patterns. A detailed example is given to illustrate the methodology. (C) 2008 Elsevier B.V. All rights reserved.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Distribution (Probability theory), Bioinformatics
Journal or Publication Title:	Computational Statistics & Data Analysis
Publisher:	Elsevier Science Ltd
ISSN:	0167-9473
Date:	15 July 2008
Volume:	Volume 52
Number:	Number 11
Number of Pages:	12
Page Range:	pp. 4879-4890
Identification Number:	10.1016/j.csda.2008.04.019
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/29590

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