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  • Waiting time distributions of competing patterns in higher-order Markovian sequences

  • Part of
  • John A. D. Aston, Donald E. K. Martin
  • Journal:
    Journal of Applied Probability / Volume 42 / Issue 4 / December 2005
    Published online by Cambridge University Press:
    14 July 2016, pp. 977-988
    Print publication:
    December 2005
    • Article
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  • Competing patterns are compound patterns that compete to be the first to occur pattern-specific numbers of times. They represent a generalisation of the sooner waiting time problem and of start-up demonstration tests with both acceptance and rejection criteria. Through the use of finite Markov chain imbedding, the waiting time distribution of competing patterns in multistate trials that are Markovian of a general order is derived. Also obtained are probabilities that each particular competing pattern will be the first to occur its respective prescribed number of times, both in finite time and in the limit.