A Theory of Truncated Inverse Sampling

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.Comment: 31 pages, no figure, revised proof

Probability Estimation with Truncated Inverse Binomial Sampling

In this paper, we develop a general theory of truncated inverse binomial sampling. In this theory, the fixed-size sampling and inverse binomial sampling are accommodated as special cases. In particular, the classical Chernoff-Hoeffding bound is an immediate consequence of the theory. Moreover, we propose a rigorous and efficient method for probability estimation, which is an adaptive Monte Carlo estimation method based on truncated inverse binomial sampling. Our proposed method of probability estimation can be orders of magnitude more efficient as compared to existing methods in literature and widely used software.Comment: 14 pages, 1 figur

A Theory of Truncated Inverse Sampling ∗

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, hypergeometrical, 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.

A Theory of Truncated Inverse Sampling ∗

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, hypergeometrical, 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.