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

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.

References in corpus (3)

• The m-th Longest Runs of Multivariate Random Sequences
• Joint distribution of rises, falls, and number of runs in random sequences
• Distributions of successions of arbitrary multisets