A theory of truncated inverse sampling

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.

KEYWORDS:

• Truncated inverse sampling
• Monte Carlo estimation
• nonasymptotic method
• sequential estimation
• confidence interval
• Uncertainty
• Bounded random variable
• Random walk

Subject Classifications:

• 62L12
• 62D05

Acknowledgements

The author would like to thank the Editor, Associated Editor and referees for their time, effort and comments in reviewing this paper. Preliminary results from this paper were posted in https://arxiv.org/abs/0810.5551 on October 30, 2008.