Joint distributions associated with countably many runs in sooner waiting time problems

Kiyoshi Inoue ()
Additional contact information
Kiyoshi Inoue: Seikei University

Metrika: International Journal for Theoretical and Applied Statistics, 2025, vol. 88, issue 6, No 15, 1126 pages

Abstract: Abstract We consider the runs enumerations in the waiting time problem related to countably many runs. Two types of random variables, i.e., the waiting time until the first occurrence of a run among the infinite number of runs and the numbers of occurrences of runs of several lengths observed at that time are of main interest. The corresponding joint distributions are investigated in terms of the probability generating functions. We provide the effective computational tools for the evaluation of the probability mass functions by making use of the potential partition polynomials. Finally, applications with numerical results are given in order to demonstrate feasibility of our theoretical results.

Keywords: Run; Enumeration schemes; Waiting times; Probability function; Probability generating function; Geometric distribution; Potential partition polynomials (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00184-024-00986-w 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:metrik:v:88:y:2025:i:6:d:10.1007_s00184-024-00986-w

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/184/PS2

DOI: 10.1007/s00184-024-00986-w

Access Statistics for this article

Metrika: International Journal for Theoretical and Applied Statistics is currently edited by U. Kamps and Norbert Henze

More articles in Metrika: International Journal for Theoretical and Applied Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().