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

Anastasios N. Arapis (), Frosso S. Makri () and Zaharias M. Psillakis ()
Additional contact information
Anastasios N. Arapis: University of Patras
Frosso S. Makri: University of Patras
Zaharias M. Psillakis: University of Patras

Journal of Statistical Distributions and Applications, 2017, vol. 4, issue 1, 1-13

Abstract: Abstract 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.

Keywords: Exact Distributions; Runs; Binary trials; Markov chain; Primary 60E05; 62E15; Secondary 60J10; 60C05 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1186/s40488-017-0080-5 Abstract (text/html)

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:jstada:v:4:y:2017:i:1:d:10.1186_s40488-017-0080-5

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/40488

DOI: 10.1186/s40488-017-0080-5

Access Statistics for this article

Journal of Statistical Distributions and Applications is currently edited by Felix Famoye and Carl Lee

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