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Multiple consecutive runs of multi-state trials: distributions of $(k_1, k_2, \dots, k_\ell)$ patterns
- Source :
- Journal of Computational and Applied Mathematics, Volume 403, 113846 (2022)
- Publication Year :
- 2024
-
Abstract
- 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.
Details
- Database :
- arXiv
- Journal :
- Journal of Computational and Applied Mathematics, Volume 403, 113846 (2022)
- Publication Type :
- Report
- Accession number :
- edsarx.2405.04004
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.cam.2021.113846