Multiple consecutive runs of multi-state trials: distributions of $(k_1, k_2, \dots, k_\ell)$ patterns
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929336846647296 |
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| author | Kong, Yong |
| author_facet | Kong, Yong |
| contents | The pattern $(k_1, k_2, \dots, k_\ell)$ is defined to have at least $k_1$ consecutive $1$'s followed by at least $k_2$ consecutive $2$'s, $\dots$, followed by at least $k_\ell$ consecutive $\ell$'s. By iteratively applying the method that was developed previously to decouple the combinatorial complexity involved in studying complicated patterns in random sequences, the distribution of pattern $(k_1, k_2, \dots, k_\ell)$ is derived for arbitrary $\ell$. Numerical examples are provided to illustrate the results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04004 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multiple consecutive runs of multi-state trials: distributions of $(k_1, k_2, \dots, k_\ell)$ patterns Kong, Yong Combinatorics Probability 05A15 (Primary) 60C05, 68R05, 68R15 (Secondary) The pattern $(k_1, k_2, \dots, k_\ell)$ is defined to have at least $k_1$ consecutive $1$'s followed by at least $k_2$ consecutive $2$'s, $\dots$, followed by at least $k_\ell$ consecutive $\ell$'s. By iteratively applying the method that was developed previously to decouple the combinatorial complexity involved in studying complicated patterns in random sequences, the distribution of pattern $(k_1, k_2, \dots, k_\ell)$ is derived for arbitrary $\ell$. Numerical examples are provided to illustrate the results. |
| title | Multiple consecutive runs of multi-state trials: distributions of $(k_1, k_2, \dots, k_\ell)$ patterns |
| topic | Combinatorics Probability 05A15 (Primary) 60C05, 68R05, 68R15 (Secondary) |
| url | https://arxiv.org/abs/2405.04004 |