On the conditional and unconditional distributions of the number of success runs on a circle with applications

Inoue, Kiyoshi; Aki, Sigeo

doi:10.1016/j.spl.2010.01.022

Cited by 8 publications

(1 citation statement)

References 34 publications

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“…It covers as particular cases the non-overlapping counting ( = 0; see Feller, 1968;Hirano, 1986;Philippou & Makri, 1986 for the linear case, and Charalambidis, 1994;Makri & Philippou, 1994;Koutras et al, 1995 for the circular case) and the overlapping counting ( = k − 1; see Ling, 1988;Hirano et al, 1991;Holst, 2009 for the linear case, and Inoue & Aki, 2010 for the the circular case).…”

Section: Introductionmentioning

confidence: 99%

Counting Runs of Ones with Overlapping Parts in Binary Strings Ordered Linearly and Circularly

Makri

Psillakis²,

Arapis³

2013

IJSP

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On a binary (0 − 1) string of length n the -overlapping counting scheme of runs of 1 s of a fixed length k is considered. According to this scheme, a run of 1s of length k which is counted may have overlapping part of length at most , 0 ≤ < k ≤ n, with the previous run of 1 s of length k that has been enumerated. The numbers of all -overlapping runs of 1 s of length k in all 2 n binary strings (linearly or circularly ordered) of length n are examined, and simple and easy to compute closed explicit expressions are provided via the probability mass function and the expected value of properly defined random variables. The numbers of binary strings of length n, ordered on a line or on a circle, with a specific number of -overlapping runs of 1s of length k are also provided via closed expressions. The numbers which are studied, are potentially useful in several scientific areas like applied probability, engineering and bioinformatics. The study is illustrated by extensive numerical examples.

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