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On mixture failure rate ordering

Author

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  • Maxim S. Finkelstein

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

  • Veronica Esaulova

Abstract

Mixtures of increasing failure rate distributions (IFR) can decrease at least in some intervals of time. Usually this property can be observed asymptotically as time tends to infinity. This is due to the fact that the mixture failure rate is ‘bent down’ compared with the corresponding unconditional expectation of the baseline failure rate, which was proved previously for some specific cases. We generalize this result and discuss the “weakest populations are dying first” property, which leads to the change in the failure rate shape. We also consider the problem of mixture failure rate ordering for the ordered mixing distributions. Two types of stochastic ordering are analyzed: ordering in the likelihood ratio sense and ordering in variances when the means are equal.

Suggested Citation

  • Maxim S. Finkelstein & Veronica Esaulova, 2005. "On mixture failure rate ordering," MPIDR Working Papers WP-2005-019, Max Planck Institute for Demographic Research, Rostock, Germany.
    • Handle: RePEc:dem:wpaper:wp-2005-019
    DOI: 10.4054/MPIDR-WP-2005-019
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    References listed on IDEAS

    as
    1. 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.
    2. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
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    JEL classification:

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

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