Annals of the Institute of Statistical Mathematics

, Volume 65, Issue 3, pp 513–527

Recursive equations in finite Markov chain imbedding

Article

DOI: 10.1007/s10463-012-0381-x

Cite this article as:
Hsieh, YF. & Wu, TL. Ann Inst Stat Math (2013) 65: 513. doi:10.1007/s10463-012-0381-x
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Abstract

In this paper, recursive equations for waiting time distributions of r-th occurrence of a compound pattern are studied via the finite Markov chain imbedding technique under overlapping and non-overlapping counting schemes in sequences of independent and identically distributed (i.i.d.) or Markov dependent multi-state trials. Using the relationship between number of patterns and r-th 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.

Keywords

Recursive equationSimple and compound patternsWaiting timeFinite Markov chain imbeddingProbability generating function

Copyright information

© The Institute of Statistical Mathematics, Tokyo 2012

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of ManitobaWinnipegCanada