Distribution Theory of Runs and Patterns Associated with a Sequence of Multi-state Trials
نویسندگان
چکیده
Runs and patterns in a sequence of Bernoulli trials and multi-state trials have broadly been used for various purposes and in many areas of statistics and applied probability. Recently, Fu and Koutras (1994) developed a new method based on finite Markov chain imbedding technique to study the exact distributions for the number of specified runs and patterns in a sequence of Bernoulli trials. In this manuscript, a “forward and backward principle” for the method of finite Markov chain imbedding is introduced to study the exact and joint distributions for the numbers of runs and patterns in a sequence of multi-state trials. Waiting time distribution for a pattern is also obtained.
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