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

Abstract

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.

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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. https://doi.org/10.1239/jap/1371648954

Information

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

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

Subjects:
Primary: 60E15
Secondary: 62P05, 90B25

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 2 • June 2013
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