Distributions of the Number of Records and the Waiting Time Distributions for the rth Record

Chang Yung-Ming (), Fu James C. () and Wu Tung-Lung ()
Additional contact information
Chang Yung-Ming: National Taitung University
Fu James C.: University of Manitoba
Wu Tung-Lung: Mississippi State University

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 3, 1-13

Abstract: Abstract Consider a sequence of independent and identically distributed random variables { $$X_t$$ X t } $$_{t = 1}^{\infty }$$ t = 1 ∞ defined on a finite state space. Our goal in this paper is to investigate the exact distributions of records associated with { $$X_t$$ X t } $$_{t = 1}^{\infty }$$ t = 1 ∞ . Based on the finite Markov chain imbedding technique, we propose a comprehensive approach to obtain the exact joint distribution of the number of records and their record values up to time n, the distribution of waiting time for the rth record, and the conditional distributions of waiting times of inter-records. In addition, we extend the results to the case where the underlying sequence { $$X_t$$ X t } $$_{t = 1}^{\infty }$$ t = 1 ∞ has an infinite state space. Examples are provided to illustrate the proposed method.

Keywords: Records; Number of records; Inter-records; Waiting times; Finite Markov chain imbedding; 60E05; 62E15 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-025-10190-6 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:metcap:v:27:y:2025:i:3:d:10.1007_s11009-025-10190-6

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-025-10190-6

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().