The preservation of likelihood ratio ordering under convolution
type: Item
instance of: scholarly article
title: The preservation of likelihood ratio ordering under convolution
zbMATH Open document ID: 0611.60047
DOI: 10.1016/0304-4149(86)90039-6
published in: Stochastic Processes and their Applications
publication date: 1986-01-01T00:00:00Z
review text: Unlike stochastic ordering \((\geq^{st})\), which is preserved under convolution (i.e., summation of independent random variables), so far it is only known that likelihood ratio ordering \((\geq^{lr})\) is preserved under convolution of log-concave \((PF_ 2)\) random variables. In this paper we define a stronger version of likelihood ratio ordering, termed shifted likelihood ratio ordering \((\geq_{\uparrow}^{lr})\) and show that it is preserved, under convolution. An application of this closure property to closed queueing network is given. Other properties of shifted likelihood ratio ordering are also discussed.
Mathematics Subject Classification ID: 60G99
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 60K20
zbMATH DE Number: 3988385
zbMATH Keywords: conditional stochastic order
zbMATH Keywords: likelihood ratio ordering
zbMATH Keywords: shifted likelihood ratio ordering
zbMATH Keywords: queueing network
author: J. George Shanthikumar
author: David D. Yao
MaRDI profile type: Publication
full work available at URL: 0304-4149(86)90039-6
OpenAlex ID: W1985376099
cites work: Polya Type Distributions, II
cites work: Q5624248
cites work: Polya Type Distributions of Convolutions
cites work: Classes of orderings of measures and related correlation inequalities. II. Multivariate reverse rule distributions
cites work: Some Results for Discrete Unimodality
cites work: Monotone matrices and monotone Markov processes
cites work: Unimodality preservation in Markov chains
cites work: Uniform stochastic ordering and related inequalities
cites work: Q3262608
cites work: Q3218851
cites work: The effect of increasing service rates in a closed queueing network
cites work: Multivariate monotone likelihood ratio and uniform conditional stochastic order
description: scientific article; zbMATH DE number 3988385