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Understanding the shape of the mixture failure rate (with engineering and demographic applications)

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  • Maxim S. Finkelstein

    (Max Planck Institute for Demographic Research, Rostock, Germany)

Abstract

Mixtures of distributions are usually effectively used for modeling heterogeneity. It is well known that mixtures of DFR distributions are always DFR. On the other hand, mixtures of IFR distributions can decrease, at least in some intervals of time. As IFR distributions often model lifetimes governed by ageing processes, the operation of mixing can dramatically change the pattern of ageing. Therefore, the study of the shape of the observed (mixture) failure rate in a heterogeneous setting is important in many applications. We study discrete and continuous mixtures, obtain conditions for the mixture failure rate to tend to the failure rate of the strongest populations and describe asymptotic behavior as t tends to infty. Some demographic and engineering examples are considered. The corresponding inverse problem is discussed.

Suggested Citation

  • Maxim S. Finkelstein, 2009. "Understanding the shape of the mixture failure rate (with engineering and demographic applications)," MPIDR Working Papers WP-2009-031, Max Planck Institute for Demographic Research, Rostock, Germany.
  • Handle: RePEc:dem:wpaper:wp-2009-031
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    File URL: http://www.demogr.mpg.de/papers/working/wp-2009-031.pdf
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    References listed on IDEAS

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    1. David Steinsaltz & Kenneth Wachter, 2006. "Understanding Mortality Rate Deceleration and Heterogeneity," Mathematical Population Studies, Taylor & Francis Journals, vol. 13(1), pages 19-37.
    2. Maxim Finkelstein & James W. Vaupel, 2006. "The relative tail of longevity and the mean remaining lifetime," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 14(7), pages 111-138, February.
    3. A. R. Thatcher, 1999. "The long-term pattern of adult mortality and the highest attained age," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(1), pages 5-43.
    4. Jorge Navarro & Pedro Hernandez, 2008. "Mean residual life functions of finite mixtures, order statistics and coherent systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(3), pages 277-298, April.
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    Cited by:

    1. Cha, Ji Hwan & Finkelstein, Maxim, 2011. "Burn-in and the performance quality measures in heterogeneous populations," European Journal of Operational Research, Elsevier, vol. 210(2), pages 273-280, April.
    2. repec:eee:reensy:v:112:y:2013:i:c:p:120-128 is not listed on IDEAS
    3. Lai, Chin-Diew & Izadi, Muhyiddin, 2012. "Generalized logistic frailty model," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1969-1977.

    More about this item

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • Z0 - Other Special Topics - - General

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