Stochastic Orders Generated by Integrals: a Unified Study
- 1 June 1997
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 29 (2) , 414-428
- https://doi.org/10.2307/1428010
Abstract
We consider stochastic orders of the following type. Let be a class of functions and let P and Q be probability measures. Then define , if ∫ ⨍ d P ≦ ∫ ⨍ d Q for all f in . Marshall (1991) posed the problem of characterizing the maximal cone of functions generating such an ordering. We solve this problem by using methods from functional analysis. Another purpose of this paper is to derive properties of such integral stochastic orders from conditions satisfied by the generating class of functions. The results are illustrated by several examples. Moreover, we show that the likelihood ratio order is closed with respect to weak convergence, though it is not generated by integrals.Keywords
This publication has 12 references indexed in Scilit:
- Stochastic Ordering and Dependence in Applied ProbabilityPublished by Springer Nature ,1995
- MR/GI/1 queues by positively correlated arrival streamJournal of Applied Probability, 1994
- Some theory of stochastic dominancePublished by Institute of Mathematical Statistics ,1991
- Multivariate stochastic orderings and generating cones of functionsPublished by Institute of Mathematical Statistics ,1991
- The preservation of likelihood ratio ordering under convolutionStochastic Processes and their Applications, 1986
- Stochastic Comparisons for Non-Markov ProcessesMathematics of Operations Research, 1986
- On maximal sets of functions compatible with a partial ordering for distribution functionsMathematische Operationsforschung und Statistik. Series Optimization, 1981
- Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributionsJournal of Multivariate Analysis, 1980
- Stochastic Inequalities on Partially Ordered SpacesThe Annals of Probability, 1977
- Ordered Families of DistributionsThe Annals of Mathematical Statistics, 1955