摘要
本文基于Taylor幂法则导出简单随机抽样,比例配额和最适配额分层抽样的理论抽样数,序贯抽样公式及其最大抽样数以及零频率和种群密度的关系。这对Taylor幂法则在实践中应用有一定意义。
In the present paper, the following formulas are deduced based on Taylor's power low:
1. theoretical sample size (n) for simple random sampling is
n=t^2/d′~2am^b or n=t^2/D^2am^(b-2),
where, a, b are parameters of Taylor's power low, d'and D, admitted errors, m, population density, and t, error of normal distribution at a certain probability level.
2. theoretical sample size for stratified random sampling in evenly proportionod share is
n=t^2/d′~2 sum W_h^2 am_h^b or n=(t/(D sum W_hm_h))~2 sum W_h^2 am_h^b,
where, w_h is proportion of no. of samples in stage h to that of the whole, m_h, the population density of stage h.
3. theoretical sample size for stratified random sampling in optimized share is
4. the sequential sampling program is
upper limit: T_0′(n)=nm_0+t(anm_0~b)^(1/2)
lower limit: T_0″(n)=nm_0—t(anm_0~b)^(1/2)
and the maximal sampling number (n_(max)) required when m=m_0 is where, m_0
n_(max)=t^2/d_0~2am_0~b
is critical population density.
5. the relationship between the froquency of nonoccurrence(p_0) and population density(m) is turned out as follows:
P_0=(am^(b-1))~(m/(1-am^(b-1))).
关键词
Taylor幂法则
抽样方法
种群密度
Taylor's power law
Theoretical sample size
Sequential sampling program
Estimating population density.
