On success runs of a fixed length in Bernoulli sequences: Exact and asymptotic results

Makri, Frosso S.; Psillakis, Zaharias M.

doi:10.1016/j.camwa.2010.12.023

Cited by 27 publications

(19 citation statements)

References 28 publications

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“…Recently, Makri and Psillakis (2011b) and provided explicit expressions for the numbers Q (β,L) n,k , β = E, G. These works simplify, extend and unify too, the results of K. Sinha andB. P. Sinha (2009, 2012) …”

Section: Associated With Ymentioning

confidence: 71%

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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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Section: Associated With Ymentioning

confidence: 71%

“…Sinha & B. P. Sinha, 2009;Makri & Psillakis, 2011a, 2011b. According to the latter scheme, a run of 1 s (1-run) is defined to be a sequence of consecutive 1 s preceded and succeeded by 0s or by nothing.…”

Section: Introductionmentioning

confidence: 99%

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

Makri

Psillakis²,

Arapis³

2013

IJSP

Self Cite

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“…Although we are aware of a few other articles which have presented lower and upper bounds (e.g., [43], [44]), we did not include them here as there seem to be some typos in the formulas presented there. For simplicity (and uniformity) the particular conditions of the different lower and upper bounds were not coded, leading to continuous simulation results over the whole range considered .…”

Section: Simulation Resultsmentioning

confidence: 94%

Review of reliability bounds for consecutive-k-out-of-n systems

Beiu

Dăuş

2014

14th IEEE International Conference on Nanotechnology

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This paper reviews many lower and upper bounds for consecutive-k-out-of-n systems presented over the last three decades. The reason is a revived interest to accurately estimate the reliability of (very) large consecutive systems, where exact calculations can be challenging. Main examples are novel nanoarchitectures targeting FinFETs, nano-magnetic and molecular technologies (where accurate estimations of reliability are of high interest), as well as their associated nanoscale communications (where the reliability of transmission needs to be assessed), which map well onto (very) large consecutive systems.Index Terms-Consecutive-k-out-of-n:F system, reliability, lower and upper bounds. NOTATIONStotal number of components of the system minimum number of consecutive faulty components which cause a system failure probability that a component works correctly probability that a component fails ( ) reliability of a consecutive-k-out-of-n:F system with component failure probability 978-1-4799-5622-7/$31.00 ©2014 IEEE

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“…video on demand) are highly encoded, decoded and eventually proceeded under security. For details, see e.g., Sinha and Sinha (2009), Makri and Psillakis (2011a) and Tabatabaei and Zivic (2015).…”

Section: Discussion and Further Studymentioning

confidence: 99%

Joint distribution of k-tuple statistics in zero-one sequences of Markov-dependent trials

2017

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We consider a sequence of n, n ≥ 3, zero (0) -one (1) Markov-dependent trials. We focus on k-tuples of 1s; i.e. runs of 1s of length at least equal to a fixed integer number k, 1 ≤ k ≤ n. The statistics denoting the number of k-tuples of 1s, the number of 1s in them and the distance between the first and the last k-tuple of 1s in the sequence, are defined. The work provides, in a closed form, the exact conditional joint distribution of these statistics given that the number of k-tuples of 1s in the sequence is at least two. The case of independent and identical 0 − 1 trials is also covered in the study. A numerical example illustrates further the theoretical results.

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On success runs of a fixed length in Bernoulli sequences: Exact and asymptotic results

Cited by 27 publications

References 28 publications

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

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

Review of reliability bounds for consecutive-k-out-of-n systems

Joint distribution of k-tuple statistics in zero-one sequences of Markov-dependent trials

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