Comparison of increasing directionally convex transformations of random vectors with a common copula

Belzunce, Félix; Suárez‐Llorens, Alfonso; Sordo, Miguel Á.

doi:10.1016/j.insmatheco.2012.02.001

Cited by 6 publications

(1 citation statement)

References 31 publications

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“…We recall that recent contributions oriented to the stochastic comparisons of random vectors, and involving increasing directionally convex transformations of the vectors, are given in [5]. See also [1], where increasing convex comparisons of generalized order statistics are given, and are extended to the increasing directionally convex comparisons of random vectors of generalized order statistics.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Comparisons of Symmetric Supermodular Functions of Heterogeneous Random Vectors

Crescenzo¹,

Frostig²,

Pellerey³

2013

J. Appl. Probab.

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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.

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Section: Introductionmentioning

confidence: 99%