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On stochastic comparisons of residual life time at random time

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  • Dewan, Isha
  • Khaledi, Baha-Eldin

Abstract

Let X1,X2,Θ and Θ′ be independent non-negative random variables. The residual life of Xi at random time Θ, that is, XiΘ=Xi−Θ∣Xi>Θ is considered. Some sufficient conditions which lead to the likelihood ratio ordering, the failure rate ordering, the reverse failure rate ordering and the mean residual life ordering between X1Θ and X2Θ are obtained and an application in queuing theory is explained. A set of conditions which lead to the same stochastic orderings between X1Θ and X1Θ′ are also derived.

Suggested Citation

  • Dewan, Isha & Khaledi, Baha-Eldin, 2014. "On stochastic comparisons of residual life time at random time," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 73-79.
    • Handle: RePEc:eee:stapro:v:88:y:2014:i:c:p:73-79
    DOI: 10.1016/j.spl.2014.01.029
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    References listed on IDEAS

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    1. Khaledi, Baha-Eldin & Shaked, Moshe, 2010. "Stochastic comparisons of multivariate mixtures," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2486-2498, November.
    2. K. T. Marshall, 1968. "Some Inequalities in Queuing," Operations Research, INFORMS, vol. 16(3), pages 651-668, June.
    3. Joag-dev, Kumar & Kochar, Subhash & Proschan, Frank, 1995. "A general composition theorem and its applications to certain partial orderings of distributions," Statistics & Probability Letters, Elsevier, vol. 22(2), pages 111-119, February.
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    Cited by:

    1. Ebrahim Amini-Seresht & Baha-Eldin Khaledi, 2015. "Multivariate stochastic comparisons of mixture models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(8), pages 1015-1034, November.
    2. Arijit Patra & Chanchal Kundu, 2021. "Stochastic comparisons and ageing properties of residual lifetime mixture models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(1), pages 123-143, August.
    3. Arijit Patra & Chanchal Kundu, 2019. "On generalized orderings and ageing classes for residual life and inactivity time at random time," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(6), pages 691-704, August.
    4. Kayid, M. & Izadkhah, S., 2015. "Characterizations of the exponential distribution by the concept of residual life at random time," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 164-169.
    5. Serkan Eryilmaz & G. Tutuncu, 2015. "Relative behavior of a coherent system with respect to another coherent system," Statistical Papers, Springer, vol. 56(2), pages 519-529, May.

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