## 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.

Original language | English |
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Pages (from-to) | 464-474 |

Number of pages | 11 |

Journal | Journal of Applied Probability |

Volume | 50 |

Issue number | 2 |

DOIs | |

State | Published - Jun 2013 |

## Keywords

- Cyclic queueing network
- Directionally convex function
- Increasing convex order
- Reliability
- Risks portfolio
- Series system
- Supermodular function

## ASJC Scopus subject areas

- Statistics and Probability
- General Mathematics
- Statistics, Probability and Uncertainty