A sufficient condition for association of a renewal process
type: Item
instance of: scholarly article
title: A sufficient condition for association of a renewal process
zbMATH Open document ID: 0608.60084
published in: The Annals of Probability
publication date: 1986-01-01T00:00:00Z
review text: Let N be a renewal point process on [0,\(\infty)\) with life time density f and consider the family \({\mathcal F}\) of random variables N(A), A Borel subset of [0,\(\infty)\). The authors prove that \({\mathcal F}\) is ''associated'' [see \textit{C. M. Newman}, Z. Wahrscheinlichkeitstheor. Verw. Geb. 59, 361- 371 (1982; Zbl 0465.60010)] provided log f is a convex function. Interesting connections to reliability theory and to particle systems are stated.
Mathematics Subject Classification ID: 60K05
Mathematics Subject Classification ID: 60K10
zbMATH DE Number: 3984272
zbMATH Keywords: associated variables
zbMATH Keywords: failure rate
zbMATH Keywords: renewal point process
zbMATH Keywords: reliability theory
zbMATH Keywords: particle systems
author: Robert Burton
author: Edward C. Waymire
reviewed by: Helmut Wegmann
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992368
OpenAlex ID: W1991158022
DOI: 10.1214/AOP/1176992368
description: scientific article; zbMATH DE number 3984272