Application Of Generalized Linear Model In Life Table Mortality

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.