This paper is concerned with developing low variance simulation estimators of probabilities related to the sum of Bernoulli random variables. It shows how to utilize an identity used in the Chen-Stein approach to bounding Poisson approximations to obtain low variance estimators. Applications and numerical examples in such areas as pattern occurrences, generalized coupon collecting, system reliability, and multivariate normals are presented. We also consider the problem of estimating the probability that a positive linear combination of Bernoulli random variables is greater than some specified value, and present a simulation estimator that is always less than the Markov inequality bound on that probability.

本文关注开发与伯努利随机变量之和相关的概率的低方差模拟估计量。它展示了如何利用 Chen-Stein 方法中使用的身份来限制泊松近似以获得低方差估计量。介绍了在模式出现、广义优惠券收集、系统可靠性和多元正态等领域的应用和数值示例。我们还考虑了估计伯努利随机变量的正线性组合大于某个指定值的概率的问题，并提出了一个始终小于该概率的马尔可夫不等式界限的模拟估计量。