On the length and the position of the minimum sequence containing all runs of ones in a Markovian binary sequence

Anastasios N. Arapis, Frosso S. Makri and Zaharias M. Psillakis

Statistics & Probability Letters, 2016, vol. 116, issue C, 45-54

Abstract: Let a sequence of binary (zero–one) trials which forms a nonhomogeneous/homogeneous Markov chain of first order with given initial probability distribution and one-step transition probability matrix. The trials are assumed to be ordered on a line. The statistics denoting the length and the position (starting, ending) of the shortest segment of the sequence containing all runs of ones, are considered. The study concerns with conditional probability distributions of the statistics given that there are at least two runs of ones in the sequence. Two application case studies related to learning experiments and DNA sequences are discussed. Illustrative numerics are presented.

Keywords: Binary trials; Runs; Markov chain; Exact distributions (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715215302285
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:116:y:2016:i:c:p:45-54

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2016.03.011

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().