Confidence Intervals for the Number Showing a Certain Characteristic in a Population when Sampling is Without Replacement
不放回抽样下总体中特定特征人数的置信区间AI 解读 ↓
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不放回抽样下总体中特定特征人数的置信区间
- 研究问题
- 从有限总体不放回随机抽样，观察样本中具有某项特征的对象数量后，如何为总体中具有该特征的总数构造置信区间？
- 方法与思路
- 作者提出两种近似区间构造方法，其中第二种考虑观测值离散性带来的修正，并通过初步考察与精确计算比较。
- 材料陈述的贡献
- 摘要称，论文系统考察该总体总数的区间估计；初步结果显示，带有离散性修正的第二种近似与精确计算较接近。
- 阅读关注点
- 应核对两种近似的推导、离散性修正的实现、精确计算基准，以及不同总体规模和抽样比例下的覆盖率。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明。近似准确性来自初步考察，摘要未提供误差范围或覆盖率保证。
原文摘要
IN A number of different sampling situations, we encounter a problem which may be stated as follows: From a population of N objects, each of which possesses or does not possess a certain characteristic, we select without replacement a random sample of n objects. Observing that m of these possess the characteristic in question, we wish to estimate the total number M having the property. This problem arises in sample surveys of human populations and in sampling inspection of manufactured articles as well as in other, less obvious, situations. It is well known (see e.g., F. F. Stephan's solution, quoted by Deming [2, p. 294]) that the maximum likelihood estimate for M is the largest integer in (m/n) (N+ 1). The problem of confidence interval estimation for M, however, seems to have escaped systematic investigation in the literature. In this paper, the problem is considered and two approximate methods are given for construction of these confidence intervals. On the basis of some preliminary investigations, it appears that the second approximation, which allows for correction for discontinuity in the observations, agrees quite closely with the exact computations.