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Sharp bounds on DMRL and IMRL classes of life distributions with specified mean

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  • Sengupta, Debasis
  • Das, Sudipta

Abstract

We obtain sharp upper and lower bounds for a reliability function with decreasing mean residual life (DMRL), in terms of its mean. The constructive proofs establish that the bounds are sharp. We also provide bounds for the IMRL class.

Suggested Citation

  • Sengupta, Debasis & Das, Sudipta, 2016. "Sharp bounds on DMRL and IMRL classes of life distributions with specified mean," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 101-107.
    • Handle: RePEc:eee:stapro:v:119:y:2016:i:c:p:101-107
    DOI: 10.1016/j.spl.2016.07.013
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    References listed on IDEAS

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    1. Dickson, D. C. M., 2001. "Lundberg Approximations for Compound Distributions with Insurance Applications. By G. E. Willmot and X. S. Lin. (Springer, 2000)," British Actuarial Journal, Cambridge University Press, vol. 7(4), pages 690-691, October.
    2. Cheng, Kan & He, Zongfu, 1989. "On proximity between exponential and DMRL distributions," Statistics & Probability Letters, Elsevier, vol. 8(1), pages 55-57, May.
    3. Bengt Klefsjö, 1982. "The hnbue and hnwue classes of life distributions," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 29(2), pages 331-344, June.
    4. Abu-Youssef, S. E., 2002. "A moment inequality for decreasing (increasing) mean residual life distributions with hypothesis testing application," Statistics & Probability Letters, Elsevier, vol. 57(2), pages 171-177, April.
    5. Abouammoh, A. & El-Neweihi, E., 1986. "Clusure of the NBUE and DMRL classes under formation of parallel systems," Statistics & Probability Letters, Elsevier, vol. 4(5), pages 223-225, August.
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    Cited by:

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    2. Khan, Ruhul Ali & Bhattacharyya, Dhrubasish & Mitra, Murari, 2021. "On some properties of the mean inactivity time function," Statistics & Probability Letters, Elsevier, vol. 170(C).

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