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Preservation of stochastic orders for random minima and maxima, with applications

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  • Xiaohu Li
  • Ming J. Zuo

Abstract

It is shown, in this note, that the right spread order and the increasing convex order are both preserved under the taking of random maxima, and the total time on test transform order and the increasing concave order are preserved under the taking of random minima. Some inequalities and preservation properties in reliability and economics are given as applications. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

Suggested Citation

  • Xiaohu Li & Ming J. Zuo, 2004. "Preservation of stochastic orders for random minima and maxima, with applications," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(3), pages 332-344, April.
    • Handle: RePEc:wly:navres:v:51:y:2004:i:3:p:332-344
    DOI: 10.1002/nav.10122
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    Cited by:

    1. Narayanaswamy Balakrishnan & Ghobad Barmalzan & Sajad Kosari, 2021. "Comparisons of Parallel Systems with Components Having Proportional Reversed Hazard Rates and Starting Devices," Mathematics, MDPI, vol. 9(8), pages 1-17, April.
    2. Bobotas, Panayiotis & Koutras, Markos V., 2024. "On the preservation of ageing properties under random maxima," Statistics & Probability Letters, Elsevier, vol. 210(C).
    3. Bobotas, Panayiotis & Koutras, Markos V., 2019. "Distributions of the minimum and the maximum of a random number of random variables," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 57-64.
    4. Nil Kamal Hazra & Asok K. Nanda & Moshe Shaked, 2014. "Some aging properties of parallel and series systems with a random number of components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(3), pages 238-243, April.

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