Abstract In this paper, we have established a new theory of truncated inverse sampling for estimating mean values of non-negative random variables such as binomial, Poisson, hyper-geometrical, and bounded variables. We have derived explicit formulas and computational methods for designing sampling schemes to ensure prescribed levels of precision and confidence for point estimators. Moreover, we have developed interval estimation methods following truncated inverse sampling procedures.

中文翻译：

---

截断逆采样理论

摘要 在本文中，我们建立了一种新的截断逆采样理论，用于估计二项式、泊松、超几何和有界变量等非负随机变量的均值。我们已经推导出了用于设计采样方案的明确公式和计算方法，以确保点估计器的精确度和置信度达到规定的水平。此外，我们开发了遵循截断逆采样程序的区间估计方法。