Multiple consecutive runs of multi-state trials: distributions of $(k_1, k_2, \dots, k_\ell)$ patterns

Yong Kong

doi:10.1016/j.cam.2021.113846

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arXiv · 2405.04004

Multiple consecutive runs of multi-state trials: distributions of $(k_1, k_2, \dots, k_\ell)$ patterns

Yong Kong

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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.

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Yong Kong. 2024-05-07. Multiple consecutive runs of multi-state trials: distributions of $(k_1, k_2, \dots, k_\ell)$ patterns. https://doi.org/10.1016/j.cam.2021.113846

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