Distribution of a Unified (k₁,k₂,…,k_m)-run

2024/10/01 by Amit Kumar, Chaturvedi, Savita, Kumar, Amit N.
Business, Management and Accounting · Decision Sciences · Mathematics · #Advanced Queuing Theory Analysis #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR) #Probability and Risk Models #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2410.00571

openalex publication_date 2024/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We explore a unified (k₁,k₂,…,k_m)-run in multi-state trials, examining its distributional properties and waiting time distribution. Our study reveals that this particular run serves as a generalization encompassing various patterns. Additionally, we discuss various results pertaining to existing patterns as special cases. To illustrate our findings, we provide an application related to DNA frequent patterns.

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