Journal of Applied Probability

Stochastic comparisons of symmetric supermodular functions of heterogeneous random vectors

Antonio Di Crescenzo, Esther Frostig, and Franco Pellerey

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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.

Article information

J. Appl. Probab., Volume 50, Number 2 (2013), 464-474.

First available in Project Euclid: 19 June 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 62P05: Applications to actuarial sciences and financial mathematics 90B25: Reliability, availability, maintenance, inspection [See also 60K10, 62N05]

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


Di Crescenzo, Antonio; Frostig, Esther; Pellerey, Franco. Stochastic comparisons of symmetric supermodular functions of heterogeneous random vectors. J. Appl. Probab. 50 (2013), no. 2, 464--474. doi:10.1239/jap/1371648954.

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