Exceedances of records

A. Castaño-Martínez (), F. López-Blázquez () and B. Salamanca-Miño ()
Additional contact information
A. Castaño-Martínez: University of Cádiz
F. López-Blázquez: University of Sevilla
B. Salamanca-Miño: University of Sevilla

Metrika: International Journal for Theoretical and Applied Statistics, 2016, vol. 79, issue 7, No 4, 837-866

Abstract: Abstract Given a sequence of random variables (rv’s) and a real function $$\psi $$ ψ , the $$\psi $$ ψ -exceedances form a subsequence consisting of those rv’s larger than a function, $$\psi $$ ψ , of the previous element of the subsequence. We present the basic distribution theory of $$\psi $$ ψ -exceedances for a sequence of independent and identically distributed rv’s. We give several examples and we study with more detail the case of exponential parents with $$\psi $$ ψ a linear function. The particular case of arithmetic exceedances is useful to describe the behavior of a type I counter when the arrival process of particles follows a non-homogeneous Poisson process. We also mention applications to destructive testing, early alert systems and the departure process of a $$M_t/D/1/1$$ M t / D / 1 / 1 queue.

Keywords: Records; Record-like random variables; Exceedances; Extreme value theory; Counters of particles; Counting processes (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00184-016-0580-1 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:79:y:2016:i:7:d:10.1007_s00184-016-0580-1

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

DOI: 10.1007/s00184-016-0580-1

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 ().