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Recursive equations in finite Markov chain imbedding
 YuFei Hsieh,
 TungLung Wu
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Abstract
In this paper, recursive equations for waiting time distributions of rth occurrence of a compound pattern are studied via the finite Markov chain imbedding technique under overlapping and nonoverlapping counting schemes in sequences of independent and identically distributed (i.i.d.) or Markov dependent multistate trials. Using the relationship between number of patterns and rth waiting time, distributions of number of patterns can also be obtained. The probability generating functions are also obtained. Examples and numerical results are given to illustrate our theoretical results.
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Inside
Within this Article
 Introduction
 Notations and preliminary results
 Recursive equations for distributions of waiting time ${\varvec{W(r}}\mathbf {,\Lambda )}$
 Numerical examples
 Summary and discussion
 References
 References
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 Title
 Recursive equations in finite Markov chain imbedding
 Journal

Annals of the Institute of Statistical Mathematics
Volume 65, Issue 3 , pp 513527
 Cover Date
 20130601
 DOI
 10.1007/s104630120381x
 Print ISSN
 00203157
 Online ISSN
 15729052
 Publisher
 Springer Japan
 Additional Links
 Topics
 Keywords

 Recursive equation
 Simple and compound patterns
 Waiting time
 Finite Markov chain imbedding
 Probability generating function
 Industry Sectors
 Authors

 YuFei Hsieh ^{(1)}
 TungLung Wu ^{(1)}
 Author Affiliations

 1. Department of Statistics, University of Manitoba, Winnipeg, MB, R3T 2N2, Canada