Convolution of the IFRA scaled-mins class
type: Item
instance of: scholarly article
title: Convolution of the IFRA scaled-mins class
zbMATH Open document ID: 0619.60086
author: Thomas H. Savits
author: Emad El-Neweihi
published in: The Annals of Probability
publication date: 1987-01-01T00:00:00Z
review text: A nonnegative random variable is said to be IFRA (increasing failure rate average) if \(P\{T>\alpha t\}\geq [P\{T>t\}]^{\alpha}\) for all \(t\geq 0\) and \(0\leq \alpha <1\). A nonnegative random vector \(T=(T_ 1,...,T_ n)\) is said to belong to the IFRA scaled-mins class if \(\min_{1\leq i\leq n}a_ iT_ i\) is IFRA for all choices \(0<a_ i\leq \infty\), \(i=1,2,...,n.\) In the paper it is shown that the IFRA scaled-mins class is closed under convolution. It is also shown that T belongs to the IFRA scaled-mins class if and only if E[H(T)\(\}\leq E^{1/\alpha}[H^{\alpha}(T/\alpha)]\) for all \(0<\alpha <1\) and all distribution functions H.
Mathematics Subject Classification ID: 60K10
Mathematics Subject Classification ID: 62N05
zbMATH DE Number: 4005298
zbMATH Keywords: reliability theory
zbMATH Keywords: increasing failure rate average
zbMATH Keywords: IFRA scaled-mins class
zbMATH Keywords: closed under convolution
reviewed by: Moshe Shaked
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992280
OpenAlex ID: W2008041911
DOI: 10.1214/AOP/1176992280
description: scientific article; zbMATH DE number 4005298