Waiting Time Problems for Patterns in a Sequence of Multi-State Trials
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 t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/11/1893 |
| _version_ | 1797549258450141184 |
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| author | Bara Kim Jeongsim Kim Jerim Kim |
| author_facet | Bara Kim Jeongsim Kim Jerim Kim |
| author_sort | Bara Kim |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T15:11:05Z |
| format | Article |
| id | doaj.art-8c6ced442bb14a548044367853832184 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:11:05Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-8c6ced442bb14a5480443678538321842023-11-20T19:18:58ZengMDPI AGMathematics2227-73902020-10-01811189310.3390/math8111893Waiting Time Problems for Patterns in a Sequence of Multi-State TrialsBara Kim0Jeongsim Kim1Jerim Kim2Department of Mathematics, Korea University, Seoul 02841, KoreaDepartment of Mathematics Education, Chungbuk National University, Chungbuk 28644, KoreaDepartment of Mathematics, University of Seoul, Seoul 02504, KoreaIn 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.https://www.mdpi.com/2227-7390/8/11/1893patternsooner waiting timestopping probabilitymatrix analytic method |
| spellingShingle | Bara Kim Jeongsim Kim Jerim Kim Waiting Time Problems for Patterns in a Sequence of Multi-State Trials Mathematics pattern sooner waiting time stopping probability matrix analytic method |
| title | Waiting Time Problems for Patterns in a Sequence of Multi-State Trials |
| title_full | Waiting Time Problems for Patterns in a Sequence of Multi-State Trials |
| title_fullStr | Waiting Time Problems for Patterns in a Sequence of Multi-State Trials |
| title_full_unstemmed | Waiting Time Problems for Patterns in a Sequence of Multi-State Trials |
| title_short | Waiting Time Problems for Patterns in a Sequence of Multi-State Trials |
| title_sort | waiting time problems for patterns in a sequence of multi state trials |
| topic | pattern sooner waiting time stopping probability matrix analytic method |
| url | https://www.mdpi.com/2227-7390/8/11/1893 |
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