Joint distribution of rises, falls, and number of runs in random sequences
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866929334672949248 |
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| author | Kong, Yong |
| author_facet | Kong, Yong |
| contents | By using the matrix formulation of the two-step approach to the distributions of runs, a recursive relation and an explicit expression are derived for the generating function of the joint distribution of rises and falls for multivariate random sequences in terms of generating functions of individual letters, from which the generating functions of the joint distribution of rises, falls, and number of runs are obtained. An explicit formula for the joint distribution of rises and falls with arbitrary specification is also obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01748 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Joint distribution of rises, falls, and number of runs in random sequences Kong, Yong Combinatorics Applications 05A15 (Primary) 60C05, 68R05, 68R15 (Secondary) By using the matrix formulation of the two-step approach to the distributions of runs, a recursive relation and an explicit expression are derived for the generating function of the joint distribution of rises and falls for multivariate random sequences in terms of generating functions of individual letters, from which the generating functions of the joint distribution of rises, falls, and number of runs are obtained. An explicit formula for the joint distribution of rises and falls with arbitrary specification is also obtained. |
| title | Joint distribution of rises, falls, and number of runs in random sequences |
| topic | Combinatorics Applications 05A15 (Primary) 60C05, 68R05, 68R15 (Secondary) |
| url | https://arxiv.org/abs/2405.01748 |