Missov Trifon I, Lenart Adam
Max Planck Institute for Demographic Research, Laboratory of Survival and Longevity, Konrad-Zuse-Str. 1, 18057 Rostock, Germany; Faculty of Economic and Social Sciences, Institute of Sociology and Demography, University of Rostock, Ulmenstr. 69, 18051 Rostock, Germany.
Theor Popul Biol. 2013 Dec;90:29-35. doi: 10.1016/j.tpb.2013.09.013. Epub 2013 Sep 29.
In a population of individuals, whose mortality is governed by a Gompertz-Makeham hazard, we derive closed-form solutions to the life-expectancy integral, corresponding to the cases of homogeneous and gamma-heterogeneous populations, as well as in the presence/absence of the Makeham term. Derived expressions contain special functions that aid constructing high-accuracy approximations, which can be used to study the elasticity of life expectancy with respect to model parameters. Knowledge of Gompertz-Makeham life expectancies aids constructing life-table exposures.
在一个个体群体中，其死亡率由冈珀茨 - 马凯姆风险率控制，我们推导出了预期寿命积分的闭式解，分别对应同质群体和伽马异质群体的情况，以及存在/不存在马凯姆项的情况。推导得出的表达式包含有助于构建高精度近似值的特殊函数，这些近似值可用于研究预期寿命相对于模型参数的弹性。了解冈珀茨 - 马凯姆预期寿命有助于构建寿命表暴露量。
