关于Gompertz–Makeham定律:一个处理人类死亡率的有用死亡率模型

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY Brazilian Journal of Probability and Statistics Pub Date : 2022-09-01 DOI:10.1214/22-bjps545
Fredy Castellares, S. Patricio, Artur J. Lemonte
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引用次数: 5

摘要

Gompertz-Makeham模型是英国精算师William M.Makeham在19世纪下半叶引入的Gompertz模型的扩展。从那时起,该模型已成功用于生物学、精算学和人口学,以描述许多物种(包括人类)的死亡率模式,确定保险政策,建立精算表和增长模型。在本文中,我们推导了Gompertz-Makeham模型在统计学、人口学和精算科学中的一些结构性质,并介绍了文献中已经介绍的其他一些性质。我们提供的所有结构特性都以闭合形式表示,这就不需要直接用数值积分来评估它们。此外,我们还研究了通过离散泊松和贝尔分布对Gompertz-Makeham模型参数的估计。特别是,我们验证了最近引入的离散Bell分布可以是泊松分布的一个有趣的替代方案,主要是因为它适合处理过度分散,而不是泊松分布。在真实死亡率数据集的基础上,我们计算了几个国家的剩余预期寿命,并验证了Gompertz-Makeham模型,特别是在Bell分布下,在实践中为处理人类死亡率提供了适当的结果。
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On the Gompertz–Makeham law: A useful mortality model to deal with human mortality
The Gompertz-Makeham model was introduced as an extension of the Gompertz model in the second half of the 19th century by the British actuary William M. Makeham. Since then, this model has been successfully used in biology, actuarial science, and demography to describe mortality patterns in numerous species (including humans), determine policies in insurance, establish actuarial tables and growth models. In this paper, we derive some structural properties of the Gompertz-Makeham model in statistics, demography, and actuarial sciences, and present some other ones already introduced in the literature. All structural properties we provide are expressed in closed-form, which eliminates the need to evaluate them with numerical integration directly. In addition, we study the estimation of the Gompertz-Makeham model parameters through the discrete Poisson and Bell distributions. In particular, we verify that the recently introduced discrete Bell distribution can be an interesting alternative to the Poisson distribution, mainly because it is suitable to deal with overdispersion, unlike the Poisson distribution. On the basis of real mortality datasets, we compute the remaining life expectancy for several countries and verify that the Gompertz-Makeham model, especially under the Bell distribution, provides proper results to deal with human mortality in practice.
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来源期刊
CiteScore
1.60
自引率
10.00%
发文量
30
审稿时长
>12 weeks
期刊介绍: The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes. More specifically, the following types of contributions will be considered: (i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects. (ii) Original articles developing theoretical results. (iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it. (iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.
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