Waiting Time Problems for Patterns in a Sequence of Multi-State Trials

Bara Kim, Jeongsim Kim and Jerim Kim
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Bara Kim: Department of Mathematics, Korea University, Seoul 02841, Korea
Jeongsim Kim: Department of Mathematics Education, Chungbuk National University, Chungbuk 28644, Korea
Jerim Kim: Department of Mathematics, University of Seoul, Seoul 02504, Korea

Mathematics, 2020, vol. 8, issue 11, 1-16

Abstract: In this paper, we investigate waiting time problems for a finite collection of patterns in a sequence of independent multi-state trials. By constructing a finite GI/M/1-type Markov chain with a disaster and then using the matrix analytic method, we can obtain the probability generating function of the waiting time. From this, we can obtain the stopping probabilities and the mean waiting time, but it also enables us to compute the waiting time distribution by a numerical inversion.

Keywords: pattern; sooner waiting time; stopping probability; matrix analytic method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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