Distributions of numbers of runs and scans on directed acyclic graphs with generation

Kiyoshi Inoue () and Sigeo Aki ()

Computational Statistics, 2013, vol. 28, issue 3, 1133-1150

Abstract: In this paper, we introduce a class of a directed acyclic graph on the assumption that the collection of random variables indexed by the vertices has a Markov property. We present a flexible approach for the study of the exact distributions of runs and scans on the directed acyclic graph by extending the method of conditional probability generating functions. The results presented here provide a wide framework for developing the exact distribution theory of runs and scans on the graphical models. We also show that our theoretical results can easily be carried out through some computer algebra systems and give some numerical examples in order to demonstrate the feasibility of our theoretical results. As applications, two special reliability systems are considered, which are closely related to our general results. Finally, we address the parameter estimation in the distributions of runs and scans. Copyright Springer-Verlag 2013

Keywords: Run; Scan; Overlapping enumeration scheme; Graphical model; Directed acyclic graph; Markov property; Lifetime; Reliability; Parameter estimation; Probability generating function (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1007/s00180-012-0349-6 (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:spr:compst:v:28:y:2013:i:3:p:1133-1150

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/180/PS2

DOI: 10.1007/s00180-012-0349-6

Access Statistics for this article

Computational Statistics is currently edited by Wataru Sakamoto, Ricardo Cao and Jürgen Symanzik

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