Paper Info
Title
Multidimensional Stochastic Ordering and Associated Random Variables
Abstract
This paper presents several relationships between the concept of associated random variables RVs and notions of stochastic ordering. The question that provides the impetus for this work is whether the association of the ℝ-valued RVs {X1, ', Xn} implies a possible stochastic ordering between the ℝn-valued RV X ≔ X1, ', Xn and its independent version X̄ ≔ X̄1, ', X̄n. This leads to results on how multidimensional probability distributions are determined by conditions on their one-dimensional marginal distributions in the event of comparison under the stochastic orderings ≤st, ≤c1, ≤cv, ≤D and ≤K. Such results have direct implications for the comparison of bounds for Fork-Join queues and for the structure of monotone functions of several variables.
Year
DOI
Venue
1989
10.1287/opre.37.3.478
Operations Research
Keywords
Field
DocType
technical report,theorems,vector analysis,queueing theory,stochastic processes,systems analysis,parallel processing,reliability,random variable,stochastic order,random variables
Discrete mathematics,Mathematical optimization,Stochastic optimization,Random variable,Stochastic process,Probability distribution,Stochastic modelling,Probability theory,Stochastic ordering,Mathematics,Marginal distribution
Journal
Volume
Issue
ISSN
37
3
0030-364X
Citations 
PageRank 
References 
6
0.93
0
Authors
2
Name
Order
Citations
PageRank
Francois Baccelli181286.80
A. M. Makowski216818.91