THE NATURAL VARIABILITY OF VITAL-RATES AND ASSOCIATED STATISTICS
THE NATURAL VARIABILITY OF VITAL-RATES AND ASSOCIATED STATISTICS
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DOI：
10.2307/2530689
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发表时间：
1986-12-01
期刊：
影响因子：
1.9
通讯作者：
BRILLINGER, DR
中科院分区：
文献类型：
--
作者：
BRILLINGER, DR
这项工作的第一个关注点是在封闭的人口或时期研究的情况下，建立粗死亡率、年龄特定死亡率、年龄标化率、标准化死亡率等的近似分布。研究发现，假设泊松出生时间和独立寿命意味着死亡人数和相应的年中人口服从二元泊松分布。词汇表被认为直接利用了结果。结果表明，在各种情况下，在给定人口规模的情况下，用均值与人口规模成正比的泊松分布来近似死亡人数的分布是令人满意的。进一步提出，存在解释变量的情况可以用死亡人数的双随机泊松分布来模拟，其平均值与人口规模成比例，解释变量的线性组合是指数函数。这种模型适用于按年龄和年份分类的加拿大女性死亡率数据。该模型的一个动态变量进一步适用于仅按年统计的女性死亡总数的时间序列。具有额外泊松变化的模型被发现导致显著改善的拟合。
The first concern of this work is the development of approximations to the distributions of crude mortality rates, age-specific mortality rates, age-standarized rates, standardized mortality ratios, and the like for the case of a closed population or period study. It is found that assuming Poisson birthtimes and independent lifetimes implies that the number of deaths and the corresponding midyear population have a bivariate Poisson distribution. The Lexis diagram is seen to make direct use of the result. It is suggested that in a variety of cases, it will be satisfactory to approximate the distribution of the number of deaths given the population size, by a Poisson with mean proportional to the population size. It is further suggested that situations in which explanatory variables are present may be modelled via a doubly stochastic Poisson distribution for the number of deaths, with mean proportional to the population size and an exponential function of a linear combination of the explanatories. Such a model is fit to mortality data for Canadian females classified by age and year. A dynamic variant of the model is further fit to the time series of total female deaths alone by year. The models with extra-Poisson variation are found to lead to substantially improved fits.