On the concentration of runs of ones of length exceeding a threshold in a Markov chain

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

Journal of Applied Statistics, 2019, vol. 46, issue 1, 85-100

Abstract: Consider a homogeneous two state (failure-success or zero-one) Markov chain of first order. The paper deals with the position and the length of the shortest segment of the first n, $ n\geq 5 $ n≥5, trials of the chain in which all runs of ones of length greater than or equal to a fixed number are concentrated. Accordingly, we define random variables denoting the starting/ending position of the first/last such runs in the chain as well as the implied distance between them. The paper provides exact closed form expressions for the probability mass function of these random variables given that the number of the considered runs in the chain is at least two. An application concerning DNA sequences is discussed. It is accompanied by numerics which exemplify further the theoretical results.

Date: 2019
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/02664763.2018.1455815 (text/html)
Access to full text is restricted to subscribers.

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:taf:japsta:v:46:y:2019:i:1:p:85-100

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/CJAS20

DOI: 10.1080/02664763.2018.1455815

Access Statistics for this article

Journal of Applied Statistics is currently edited by Robert Aykroyd

More articles in Journal of Applied Statistics from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().