Improved Sequential Stopping Rule for Monte Carlo Simulation

TL;DR

This paper enhances the negative-binomial Monte Carlo method by broadening the confidence level guarantees for estimating an unknown probability, making the estimator more widely applicable across different interval ranges.

Contribution

It provides an improved theoretical analysis that extends confidence level guarantees for the negative-binomial Monte Carlo estimator across a wider range of intervals.

Findings

Confidence level exceeds asymptotic value for broader intervals

Applicability of the estimator is extended to more cases

Conditions for guaranteed confidence levels are relaxed

Abstract

This paper presents an improved result on the negative-binomial Monte Carlo technique analyzed in a previous paper for the estimation of an unknown probability p. Specifically, the confidence level associated to a relative interval [p/\mu_2, p\mu_1], with \mu_1, \mu_2 > 1, is proved to exceed its asymptotic value for a broader range of intervals than that given in the referred paper, and for any value of p. This extends the applicability of the estimator, relaxing the conditions that guarantee a given confidence level.