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On the shape of the mean residual lifetime function

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  • M. S. Finkelstein

Abstract

Some general properties of the mean residual life (MRL) function are studied. The analysis is based on the shape of the corresponding failure rate. The conditions under which the failure rate and the reciprocal to the MRL function have asymptotically equivalent behaviour as t→∞ are discussed. The simplest non‐monotone shapes of the functions under consideration (bathtub and upside down bathtub) are also considered. The MRL functions for mixtures of distributions are described via the corresponding conditional probability density functions. The direct proportional model of mixing is characterized and some asymptotic results on the shape of the mixture MRL are obtained. Some simple examples are given. Copyright © 2002 John Wiley & Sons, Ltd.

Suggested Citation

  • M. S. Finkelstein, 2002. "On the shape of the mean residual lifetime function," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 18(2), pages 135-146, April.
    • Handle: RePEc:wly:apsmbi:v:18:y:2002:i:2:p:135-146
    DOI: 10.1002/asmb.461
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    Cited by:

    1. Mohamed Kayid & Mansour Shrahili, 2023. "Characterization Results on Lifetime Distributions by Scaled Reliability Measures Using Completeness Property in Functional Analysis," Mathematics, MDPI, vol. 11(6), pages 1-15, March.
    2. Ruiqing Miao & David A. Hennessy & Hongli Feng, 2022. "Grassland easement evaluation and acquisition with uncertain conversion and conservation returns," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 70(1), pages 41-61, March.
    3. Belzunce, Felix & Ortega, Eva-Maria & Ruiz, Jose M., 2007. "On non-monotonic ageing properties from the Laplace transform, with actuarial applications," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 1-14, January.

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