Joint distributions of numbers of runs of specified lengths on directed trees

Kiyoshi Inoue () and Sigeo Aki
Additional contact information
Kiyoshi Inoue: Seikei University
Sigeo Aki: Kansai University

Statistical Papers, 2018, vol. 59, issue 1, No 11, 249-269

Abstract: Abstract In this paper, we consider exact joint distributions of numbers of success runs of specified lengths on a Markov directed tree under $$\ell $$ ℓ -overlapping enumeration schemes. Methods for deriving the probability generating functions of the joint distribution are presented. We extend the exact distribution theory of runs based on sequences to runs based on directed trees. Some numerical results for the run statistics are given in order to illustrate the computational aspects and the feasibility of our theoretical results. The reliability systems and lifetime distributions are considered. Our general results are applied to reliability systems and lifetime distributions. Finally, we discuss parametric estimation problems based on the lifetimes of the systems.

Keywords: Probability generating function; Success run; Markov directed tree; Reliability; Lifetime; Estimation; Primary 60E05; Secondary 60J10 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00362-016-0762-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:stpapr:v:59:y:2018:i:1:d:10.1007_s00362-016-0762-y

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-016-0762-y

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

More articles in Statistical Papers from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().