Comparison and bounds for functionals of future lifetimes consistent with life tables |
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Authors: | Christiane Barz,Alfred Mü ller |
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Affiliation: | a UCLA Anderson School of Management, 110 Westwood Plaza, Los Angeles, CA 90095, USAb Universität Siegen, Department Mathematik, Walter-Flex-Str. 3, 57072 Siegen, Germany |
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Abstract: | We derive a new crossing criterion of hazard rates to identify a stochastic order relation between two random variables. We apply this crossing criterion in the context of life tables to derive stochastic ordering results among three families of fractional age assumptions: the family of linear force of mortality functions, the family of quadratic survival functions and the power family. Further, this criterion is used to derive tight bounds for functionals of future lifetimes that exhibit an increasing force of mortality with given one-year survival probabilities. Numerical examples illustrate our findings. |
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Keywords: | C02 IM10 IB11 Stochastic order Fractional age assumptions Increasing mortality rate Bounds |
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