The rank of the current lifetime
type: Item
instance of: scholarly article
title: The rank of the current lifetime
zbMATH Open document ID: 0805.60088
DOI: 10.1016/0167-7152(94)90014-0
published in: Statistics \& Probability Letters
publication date: 1995-01-29T00:00:00Z
review text: The rank \(R_ t\) of the current lifetime of a component is denoted as \(R_ t= \#\{1\leq i\leq N_ t\): \(X_ i> X_{N_ t+1}\}\), where \(\{X_ i\}\) denotes the lifetimes (interarrival times) of a standard renewal process \(\{N_ t\), \(t\geq 0\}\). The asymptotic distribution of the relative rank \(R_ t/N_ t\) as \(t\to\infty\) is obtained. This result is shown to exhibit another feature of the inspection paradox.
Mathematics Subject Classification ID: 60K05
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 633494
zbMATH Keywords: current lifetime
zbMATH Keywords: asymptotic distribution
zbMATH Keywords: relative rank
zbMATH Keywords: inspection paradox
author: Rudolf Grübel
reviewed by: S. Kalpakam
MaRDI profile type: Publication
full work available at URL: 0167-7152(94)90014-0
OpenAlex ID: W2090275468
cites work: An asymptotic theory for empirical reliability and concentration processes
cites work: Q5624436
cites work: Convergence theorems for empirical Lorenz curves and their inverses
description: scientific article; zbMATH DE number 633494