Translator Disclaimer
June 2013 Stochastic comparisons of symmetric supermodular functions of heterogeneous random vectors
Antonio Di Crescenzo, Esther Frostig, Franco Pellerey
Author Affiliations +
J. Appl. Probab. 50(2): 464-474 (June 2013). DOI: 10.1239/jap/1371648954


Consider random vectors formed by a finite number of independent groups of independent and identically distributed random variables, where those of the last group are stochastically smaller than those of the other groups. Conditions are given such that certain functions, defined as suitable means of supermodular functions of the random variables of the vectors, are supermodular or increasing directionally convex. Comparisons based on the increasing convex order of supermodular functions of such random vectors are also investigated. Applications of the above results are then provided in risk theory, queueing theory, and reliability theory, with reference to (i) net stop-loss reinsurance premiums of portfolios from different groups of insureds, (ii) closed cyclic multiclass Gordon-Newell queueing networks, and (iii) reliability of series systems formed by units selected from different batches.


Download Citation

Antonio Di Crescenzo. Esther Frostig. Franco Pellerey. "Stochastic comparisons of symmetric supermodular functions of heterogeneous random vectors." J. Appl. Probab. 50 (2) 464 - 474, June 2013.


Published: June 2013
First available in Project Euclid: 19 June 2013

MathSciNet: MR3102493
zbMATH: 1274.60051
Digital Object Identifier: 10.1239/jap/1371648954

Primary: 60E15
Secondary: 62P05 , 90B25

Keywords: cyclic queueing network , directionally convex function , increasing convex order , reliability , risks portfolio , series system , Supermodular function

Rights: Copyright © 2013 Applied Probability Trust


This article is only available to subscribers.
It is not available for individual sale.

Vol.50 • No. 2 • June 2013
Back to Top