Stochastic majorization of random variables by proportional equilibrium rates
- 1 December 1987
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 19 (4) , 854-872
- https://doi.org/10.2307/1427105
Abstract
The equilibrium raterYof a random variableYwith support on non-negative integers is defined byrY(0) = 0 andrY(n) =P[Y = n –1]/P[Y–n],Let(j= 1, …,m;i= 1,2) be 2mindependent random variables that have proportional equilibrium rates with(j= 1, …,m;i= 1, 2) as the constant of proportionality. When the equilibrium rate is increasing and concave [convex] it is shown that, …,) majorizesimplies, …,for all increasing Schur-convex [concave] functionswhenever the expectations exist. In addition if, (i= 1, 2), thenKeywords
This publication has 24 references indexed in Scilit:
- Stochastic convexity and its applicationsAdvances in Applied Probability, 1988
- The effect of increasing service rates in a closed queueing networkJournal of Applied Probability, 1986
- The optimality of balancing workloads in certain types of flexible manufacturing systemsEuropean Journal of Operational Research, 1985
- The convexity of the mean queue size of the M/M/c queue with respect to the traffic intensityJournal of Applied Probability, 1983
- Uniform stochastic ordering and related inequalitiesThe Canadian Journal of Statistics / La Revue Canadienne de Statistique, 1982
- Models for Understanding Flexible Manufacturing SystemsA I I E Transactions, 1980
- Stochastic Inequalities on Partially Ordered SpacesThe Annals of Probability, 1977
- Increasing Properties of Polya Frequency FunctionThe Annals of Mathematical Statistics, 1965
- Polya Type Distributions of ConvolutionsThe Annals of Mathematical Statistics, 1960
- On Random Variables with Comparable PeakednessThe Annals of Mathematical Statistics, 1948