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Increasing convex order on generalized aggregation of SAI random variables with applications

Part of: Mathematical economics Distribution theory - Probability

Published online by Cambridge University Press:  15 September 2017

Xiaoqing Pan  and
Xiaohu Li
Xiaoqing Pan*
Affiliation:
Medical College of Wisconsin and University of Science and Technology of China
Xiaohu Li*
Affiliation:
Stevens Institute of Technology
*
* Postal address: Department of Physiology and Cancer Center, Medical College of Wisconsin, Milwaukee, WI 53226, USA.
** Postal address: Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ 07030, USA. Email address: [email protected]
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Abstract

In this paper we study general aggregation of stochastic arrangement increasing random variables, including both the generalized linear combination and the standard aggregation as special cases. In terms of monotonicity, supermodularity, and convexity of the kernel function, we develop several sufficient conditions for the increasing convex order on the generalized aggregations. Some applications in reliability and risks are also presented.

Keywords

Arrangement increasingcoverage limitdeductiblegeneralized linear combinationmajorizationsubmodularweighted k-out-of-n system

MSC classification

Primary: 91B16: Utility theory 91B30: Risk theory, insurance
Secondary: 60E15: Inequalities; stochastic orderings
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 3 , September 2017 , pp. 685 - 700
Copyright
Copyright © Applied Probability Trust 2017 

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