2022/11/01 by Jung‐Taek Oh, Oh, Jungtaek
Biochemistry, Genetics and Molecular Biology · #Advanced biosensing and bioanalysis techniques #Combinatorics (math.CO) #DNA and Biological Computing #DNA and Nucleic Acid Chemistry #FOS: Computer and information sciences #FOS: Mathematics #Other Statistics (stat.OT) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2211.00774
openalex publication_date 2022/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
From a mathematical and statistical point of view, a segment of a DNA strand can be viewed as a sequence of four-state (A, C, G, T) trials. We consider distributions of runs and patterns related to run lengths of multi-state sequences, especially for four states (A, B, C, D). Let X1, X2, … be a sequence of four state i.i.d. trials taking values in the set \mathscrS=\A, B, C, D\ of four symbols with probability P(A)=Pa, P(B)=Pb, P(C)=Pc and P(D)=Pd, respectively. In this paper, we obtain exact formulae for the probability distribution function for runs of B's the discrete distribution of order k, longest run statistics, shortest run statistics, waiting time distribution and the distribution of run lengths.