【作者】 刘昕；

【导师】 郑文瑞；

【作者基本信息】 吉林大学 ， 保险（专业学位）， 2018， 硕士

【摘要】 生命表又名死亡率表,是人们根据大数法则,同时运用概率论与数理统计方法,记录一定数量的被观察者自出生(一定年龄)到全部死亡(一定年龄)时间段的生存和死亡情况,并以一定方式反应生死概率的形式.由于寿险精算所涉及的风险具有三个性质:1.客观存在;2.不确定;3.可预测.因此,以往年被观察人的生存率与死亡率来预测现在、将来相似群体的被观察者的生存和死亡概率的近似值,所以准确的生命表支持将至关重要.通过查询人口统计年鉴,我们可以获得大量死亡率初始数据,我们需要对初始数据进行处理,如参数修匀,即假设死亡率近似服从某种分布,求出该分布的参数,算出参数修匀后的死亡率,作为经验生命表中的死亡率.本文讨论的是广义线性模型在我国国民生命表死亡率修匀中的应用,首先查阅中国统计年鉴整理出全国不同年龄段男性死亡人口数据.将年龄和年份因子当做自变量,死亡率当做响应变量,画出男性死亡率、年龄、年份的三维图,分析研究男性死亡率和年龄因子以及年份因子之间的关系.最终选取广义线性模型中的泊松回归模型以及负二项回归模型对不同年份0-89岁男性人口的死亡率进行拟合.拟合的具体步骤如下:首先列出死亡率关于模型参数的极大似然方程组,其次通过相关统计软件可以求解此方程组,其原理是通过牛顿-拉普森迭代法解非线性极大似然方程组,得到参数后进而对死亡率初始数据进行参数修匀,最后再对两种模型拟合的效果进行比较,选定最优模型.更多还原

【Abstract】 Life table is also called mortality table.It is used to record the survival and death of a certain amount of the observables from birth(or a certain age)to death(or a certain age),and it can express the probability of survival and death by some models.According to three properties(objective existence,uncertainty and predictable)in actu-arial calculation,We always use the previous survival rate and mortality rate to predict the survival and death condition of similar population.So an accurate life table is vital.After looking up the Statistical yearbook of population,we obtain a lot of initial data of mortality,we make use of some measures to deal with the initial data,such as smoothing parameters.We assume that mortality rates similar to obey a certain distribution,estimate the parameters of the distribution,calculatethe mortality rate as the life table of mortality depend on the smoothing parameter.We discussed the use of GLM for smoothing the national life table mortality rate in this article.Firstly we look up the amount of the male in different ages(according to China statistical year book).Consider age and year factors as independent variables,mortality as response variables,draw a three dimensional figure death about rate,age,years,analysis the relationship between the mortality,the age factor and year factor.Finally we choose Poisson Regression Model and Negative Binomial Regression Model in Generalized Linear Models to fit the gender-related mortality of people who aged from 0 years-old to 89 years-old in different vinages.The specific steps of fitting are as follows:First of all establish maximum likelihood equations about mortality with model parameters,then use relevant statistical software to solve the equations,the principle is using Newton-Raphson iteration method to solve a non-linear maximum likelihood equations,after obtaining the initial data we can smooth the mor-tality.In the end we need to compare the effect of two kinds of model fitting,select the optimal model.更多还原