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Some new bounds for the mean value function of the residual lifetime process

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  • Pekalp, Mustafa Hilmi

Abstract

In this study, mean residual lifetime (MRL) function of the residual lifetime process is investigated. Various two-sided bounds are obtained for this function by using the monotone convergence of the sequence of the functions. Since many important features of any stochastic process depend on classifications of distributions, improved bounds are found for MRL function by considering the taxonomy of the distributions. Moreover, some new bounds are achieved by using the asymptotic expression of MRL function and its boundary relation with the MRL of a single component at age t. Three examples are given to illustrate the results proposed.

Suggested Citation

  • Pekalp, Mustafa Hilmi, 2022. "Some new bounds for the mean value function of the residual lifetime process," Statistics & Probability Letters, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:stapro:v:187:y:2022:i:c:s0167715222000803
    DOI: 10.1016/j.spl.2022.109497
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    References listed on IDEAS

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    1. Politis, Konstadinos, 2005. "Bounds for the probability and severity of ruin in the Sparre Andersen model," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 165-177, April.
    2. Chadjiconstantinidis, Stathis & Politis, Konstadinos, 2007. "Two-sided bounds for the distribution of the deficit at ruin in the renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 41-52, July.
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    4. Losidis, Sotirios & Politis, Konstadinos, 2017. "A two-sided bound for the renewal function when the interarrival distribution is IMRL," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 164-170.
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