参数Bootstrap方法在全年龄人口死亡模型中的应用

The Application of Bootstrap Parameter in All Ages Mortality Models

在全年龄人口死亡模型中,较为著名的有Heligman及Pollard(1980)提出的具有8个参数的死亡率模型,也有Carriere(1992)分析美国人口死亡规律所提出的由四个生存函数:Gompertz分布、逆Gompertz分布、Weibull分布和逆Weibull分布所组成的混合参数生存模型。本文试图将He-ligman-Pollard模型与Carriere模型应用于中国分年龄、分性别的全年龄人口死亡数据,先借助R软件或Excel软件估计两种参数模型中的参数,然后利用参数Bootstrap方法计算所估参数的标准误、偏度、t统计量、置信区间等,并以此评估模型拟合的精度。最后,针对中国人口分年龄、分性别的死亡数据,提出相应的模型拟合建议。

In all ages mortality models, the two better known models are those put forward by Heligman and Pollard （1980） and Carriere （1992）. The former is a mortality model of 8 parameters, and the latter is a mixture of the four survival distributions：Gompertz, Inverse Gompertz, Weibull and Inverse Weibull, which are used to model the mor- tality curve of a population. This article attempted to fit the two all ages mortality models to China＇s population death data by gender and by age, first with the help of R software or Excel software to estimate all the parameters of the two parametric models, and then assessing the accuracy of the two models by calculating the parametric Bootstrap estimates of standard error, bias, t-statistic, confidence intervals of all estimated parameters. At last, this article sug- gested the corresponding model fitting wtih China＇s population death data.