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Stochastic comparisons of random minima and maxima from life distributions

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  • Bartoszewicz, Jaroslaw

Abstract

Recently Shaked and Wong (J. Appl. Probab. 34 (1997) 420) obtained stochastic comparison results involving random minima and maxima of a sequence of non-negative independent random variables. In this paper we derive some relations between the random extremes and classes of life distributions with monotone hazard rate. Preservation of some stochastic orders under the taking of random extremes is established. Results of Shaked (in: Patil et al. (Eds.), Statistical Distributions in Scientific Work, Reidel, Dordrecht, 1975, p. 363) are extended and a new proof of a result of Shaked and Wong (1997) is given.

Suggested Citation

  • Bartoszewicz, Jaroslaw, 2001. "Stochastic comparisons of random minima and maxima from life distributions," Statistics & Probability Letters, Elsevier, vol. 55(1), pages 107-112, November.
    • Handle: RePEc:eee:stapro:v:55:y:2001:i:1:p:107-112
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    References listed on IDEAS

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    1. Alzaid, Abdulhamid A. & Proschan, Frank, 1992. "Dispersivity and stochastic majorization," Statistics & Probability Letters, Elsevier, vol. 13(4), pages 275-278, March.
    2. Bartoszewicz, Jaroslaw, 2000. "Stochastic orders based on the Laplace transform and infinitely divisible distributions," Statistics & Probability Letters, Elsevier, vol. 50(2), pages 121-129, November.
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    Cited by:

    1. 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.
    2. Ibrahim Ahmad & Mohamed Kayid, 2007. "Reversed preservation of stochastic orders for random minima and maxima with applications," Statistical Papers, Springer, vol. 48(2), pages 283-293, April.
    3. Al-Mutairi, D.K. & Ghitany, M.E. & Gupta, Ramesh C., 2011. "Estimation of reliability in a series system with random sample size," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 964-972, February.
    4. M. Kayid & S. Izadkhah & Ming J. Zuo, 2017. "Some results on the relative ordering of two frailty models," Statistical Papers, Springer, vol. 58(2), pages 287-301, June.
    5. Bobotas, Panayiotis & Koutras, Markos V., 2024. "On the preservation of ageing properties under random maxima," Statistics & Probability Letters, Elsevier, vol. 210(C).
    6. 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.
    7. Shovan Chowdhury & Amitava Mukherjee & Asok K. Nanda, 2014. "On A Two-Parameter Discrete Distribution And Its Applications," Working papers 144, Indian Institute of Management Kozhikode.
    8. 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.
    9. Miroslav Ristić & Debasis Kundu, 2015. "Marshall-Olkin generalized exponential distribution," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 317-333, December.

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