分数年龄假设的新方法:Kriging模型

A New Method for Fractional Age Assumptions based on Kriging Model

在生存函数的计算中,生命表只提供了整数年龄上的值。当计算非整数年龄上的生存函数时就需要进行分数年龄假设。经典的分数年龄假设在数学上容易处理,但却容易导致死力函数不连续,更重要的是无法保证其在分数年龄上估计的精确性。分数年龄假设本质上是一种插值技术。本研究尝试将一种插值性能优越的Kriging模型引入到分数年龄假设中,对整数年龄上的生存函数进行插值,并基于良好拟合的生存函数进一步构建死力函数及平均余命函数。基于Kriging模型的分数年龄假设的有效性通过了Makeham法则下的生存函数的验证,结果表明,Kriging模型的插值性能远胜过经典的分数年龄假设模型。

Life tables just provide the values of survival function at exact integer ages. Actuaries often make fractional age assumptions （FAAs） to value survival function at non-integer ages. Classic FAAs have the advantage of being easily treated mathematically, but it is easy for them to produce non-continuity for force of mortality. The most of apparent disadvantages for them is that they can not guarantee to capture precisely the real trends of the survival functions. Actually, an FAA is an interpolation technique. In this study, we try to introduce the well-performance Kriging model to FAA. After fitting the survival function at integer ages, we use the precisely-constructed survival function to build the force of mortality and the life expectancy. The validity of the introduced model is evaluated by a Makehamized survival function. The experimental results show that the interpolation performance of Kriging model greatly outperforms the traditional FAAs.