Computing waiting time probabilities related to $$ (k_{1},k_{2},\ldots,k_{l})$$ ( k 1, k 2, …, k l ) pattern

Stathis Chadjiconstantinidis and Serkan Eryilmaz ()
Additional contact information
Stathis Chadjiconstantinidis: University of Piraeus
Serkan Eryilmaz: Atilim University

Statistical Papers, 2023, vol. 64, issue 5, No 1, 1373-1390

Abstract: Abstract For a sequence of multi-state trials with l possible outcomes denoted by $$ \left\{ 1,2,\ldots ,l\right\} $$ 1 , 2 , … , l , let E be the event that at least $$k_{1}$$ k 1 consecutive 1s followed by at least $$k_{2}$$ k 2 consecutive 2s,..., followed by at least $$k_{l}$$ k l consecutive ls. Denote by $$T_{r}$$ T r the number of trials for the rth occurrence of the event E in a sequence of multi-state trials. This paper studies the distribution of the waiting time random variable $$T_{r}$$ T r when the sequence consists of independent and identically distributed multi-state trials. In particular, distributional properties of $$ T_{r}$$ T r are examined via matrix-geometric distributions.

Keywords: Matrix-geometric distribution; Pattern; Probability generating function; Runs; Waiting time (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00362-022-01351-7 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:64:y:2023:i:5:d:10.1007_s00362-022-01351-7

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

DOI: 10.1007/s00362-022-01351-7

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 ().