A Theory of Truncated Inverse Sampling

TL;DR

This paper introduces a new framework called truncated inverse sampling for estimating the means of various non-negative random variables, providing explicit formulas and methods for precise and confident estimation.

Contribution

It develops a comprehensive theoretical framework and computational tools for truncated inverse sampling, enhancing estimation accuracy for multiple types of non-negative variables.

Findings

Derived explicit formulas for sampling schemes

Developed interval estimation methods

Ensured prescribed precision and confidence levels

Abstract

In this paper, we have established a new framework 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.