使用伯氏多項式估計及預測死亡率

Estimation and Prediction for Mortality Rate using Bernstein Polynomials

洪立軒(Li-Syuan Hong)

指導教授 ： 吳裕振 ； 簡莉珠

中原大學/理學院/應用數學研究所/碩士(2018年)

https://doi.org/10.6840/cycu201800213

摘要

本研究利用二維度伯氏多項式來描述及預測某特定年代及年齡族群下 的死亡率｡我們主要利用形狀限制(shape restricted)二維度伯氏多項式來建 立數學模型,並使用模擬退火(simulated annealing)演算法尋找模型參數的 最大概似估計量,以便於我們能估計及預測某特定年代及年齡族群下的死亡 率｡ 我們利用了模擬研究及實際資料分析,藉由比較現有方法(P-spline 法,Lee-Carter模型),以檢視我們的方法有效性,在實際資料部分,藉由人類死 亡資料庫(http://www.mortality.org/),所提供的瑞典死亡率資料作為範例｡

關鍵字

死亡率 ； 估計及預測 ； 伯氏多項式 ； 最大概似法 ； 模擬退火法

並列摘要

In this study, the two-dimensional Bernstein polynomials are used to describe and predict mortality rates for the some particular years and age groups that we are interested in. We mainly use the shape-restricted two-dimensional Bernstein polynomials to build a mathematical model and use the simulated annealing algorithm to find the maximum likelihood estimates of the model parameters, in order to estimate and predict the mortality rate for the some particular years and age groups that we are interested in. We use the analysis of the simulated datasets and real data examples to examine the effectiveness of our method by comparing the existing methods, the P-spline smoothing method and the Lee-Carter model. The Swedish mortality data from the Human Mortality Database (http://www.mortality.org/) are illustrated in the analysis of the real data examples.

並列關鍵字

Mortality ； Estimation and estimation ； Bernstein polynomials ； Maximum likelihood ； Simulated annealing

參考文獻

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