A stochastic population projection system based on general age-dependent branching processes
A stochastic population projection system based on general age-dependent branching processes
复制标题
基于一般年龄相关分支过程的随机人口预测系统
DOI：
10.2307/3214054
复制
发表时间：
1987
影响因子：
1
通讯作者：
G. Pickens
中科院分区：
文献类型：
--
作者：
C. Mode;M. E. Jacobson;G. Pickens
随机种群过程的算法基于离散时间中一般与年龄相关的分支过程和时间非均匀进化规律的假设，通过使用涉及出生队列和随机变量的随机总和的基本随机函数的新表示来开发。新算法提供了计算过程的平均年龄结构以及方差和协方差的能力，测量平均值的变化。提出了四种探索性人口预测，测试算法对时间同质进化定律情况的影响。还提出了将单位人口预测的均值和方差函数扩展到任意初始人口规模的公式。这些公式表明，在具有非随机进化规律的种群过程中，当初始种群规模较大时，平均函数的随机波动可以忽略不计。将这些公式进一步扩展到随机进化定律的情况表明，即使对于大量初始种群，平均函数的随机波动也可能很重要。
Algorithms for a stochastic population process, based on assumptions underlying general age-dependent branching processes in discrete time with time inhomogeneous laws of evolution, are developed through the use of a new representation of basic random functions involving birth cohorts and random sums of random variables. New algorithms provide a capability for computing the mean age structure of the process as well as variances and covariances, measuring variation about means. Four exploratory population projections, testing the implications of the algorithms for the case of time-homogeneous laws of evolution, are presented. Formulas extending mean and variance functions for unit population projections to an arbitrary initial population size are also presented. These formulas show that, in population processes with non-random laws of evolution, stochastic fluctuations about the mean function are negligible when initial population size is large. Further extensions of these formulas to the case of randomized laws of evolution suggest that stochastic fluctuations about the mean function can be significant even for large initial populations.