Gamma-Gompertz life expectancy at birth
Gamma-Gompertz life expectancy at birth
复制标题
DOI：
10.4054/demres.2013.28.9
复制
发表时间：
2013-02-12
影响因子：
2.1
通讯作者：
Missov, Trifon I.
中科院分区：
文献类型：
--
作者：
Missov, Trifon I.
γ-Gompertz乘性脆弱性模型是应用于成人和老年人死亡率数据的最常见的参数模型。由此产生的预期寿命到目前为止只被数值计算过。γ-Gompertz分布的性质还没有被彻底研究过。本文的重点是阐明它的第一个时刻，或者从人口统计学上讲，描述死亡率的伽马-Gompertz力导致的预期寿命。本文提供了一个精确的伽玛-Gompertz出生时预期寿命的公式和一个更简单的高精度近似值，可用于实际计算方便。此外，本文还比较了实际（寿命表）和基于模型（gamma-Gompertz）的预期寿命，以评估gamma-Gompertz死亡率机制未捕获（或高估）多少年的预期寿命。出生时gamma-Gomeprtz预期寿命的COMMENTSA闭合表达式包含一个特殊的（超几何）函数。它有助于评估γ-Gompertz参数对预期寿命值的影响。本文表明，高精度的近似，可以通过假设一个整数值的伽玛分布的形状参数。对瑞典女性基于模型的预期寿命和实际预期寿命进行历史比较，发现从1950年起差距缩小到约2年。看看30岁和50岁的剩余预期寿命，我们看到这种差距几乎消失了。
BACKGROUNDThe gamma-Gompertz multiplicative frailty model is the most common parametric model applied to human mortality data at adult and old ages. The resulting life expectancy has been calculated so far only numerically.OBJECTIVEProperties of the gamma-Gompertz distribution have not been thoroughly studied. The focus of the paper is to shed light onto its first moment or, demographically speaking, characterize life expectancy resulting from a gamma-Gompertz force of mortality. The paper provides an exact formula for gamma-Gompertz life expectancy at birth and a simpler high-accuracy approximation that can be used in practice for computational convenience. In addition, the article compares actual (life-table) to model-based (gamma-Gompertz) life expectancy to assess on aggregate how many years of life expectancy are not captured (or overestimated) by the gamma-Gompertz mortality mechanism.COMMENTSA closed-form expression for gamma-Gomeprtz life expectancy at birth contains a special (the hypergeometric) function. It aids assessing the impact of gamma-Gompertz parameters on life expectancy values. The paper shows that a high-accuracy approximation can be constructed by assuming an integer value for the shape parameter of the gamma distribution. A historical comparison between model-based and actual life expectancy for Swedish females reveals a gap that is decreasing to around 2 years from 1950 onwards. Looking at remaining life expectancies at ages 30 and 50, we see this gap almost disappearing.