CAJ | 학술논문

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.
재생존함수적계산중,생명표지제공료정수년령상적치.당계산비정수년령상적생존함수시취수요진행분수년령가설.경전적분수년령가설재수학상용역처리,단각용역도치사력함수불련속,경중요적시무법보증기재분수년령상고계적정학성.분수년령가설본질상시일충삽치기술.본연구상시장일충삽치성능우월적Kriging모형인입도분수년령가설중,대정수년령상적생존함수진행삽치,병기우량호의합적생존함수진일보구건사력함수급평균여명함수.기우Kriging모형적분수년령가설적유효성통과료Makeham법칙하적생존함수적험증,결과표명,Kriging모형적삽치성능원성과경전적분수년령가설모형.
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.