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On the preservation of ageing properties under random maxima

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  • Bobotas, Panayiotis
  • Koutras, Markos V.

Abstract

The preservation of increasing failure rate, increasing failure rate average, and new better than used properties under random maxima is studied, by unifying, completing, correcting, extending and/or generalizing existing results in the literature. As a by-product, the previous ageing notions are also introduced for a nonnegative mixed-type random variable.

Suggested Citation

  • Bobotas, Panayiotis & Koutras, Markos V., 2024. "On the preservation of ageing properties under random maxima," Statistics & Probability Letters, Elsevier, vol. 210(C).
  • Handle: RePEc:eee:stapro:v:210:y:2024:i:c:s0167715224000804
    DOI: 10.1016/j.spl.2024.110111
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Bartoszewicz, Jaroslaw, 2001. "Stochastic comparisons of random minima and maxima from life distributions," Statistics & Probability Letters, Elsevier, vol. 55(1), pages 107-112, November.
    4. P.C. Consul, 1984. "On The Distributions Of Order Statistics For A Random Sample Size," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 38(4), pages 249-256, December.
    5. 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.
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