置信分布的贝塔分布近似及其在可靠性统计中的应用

在复杂系统可靠性综合评估方法研究中,利用β分布来近似区间0,1]上的各种概率分布是一种常用的工程方法,并被许多系统可靠性综合评估方法所采用。工程中常用的β分布近似方法有二阶矩法和点估计下限法。为了减少近似误差,本文在文献1]的基础上,对文献1]中提出的β分布近似的两点法进行了深入研究,证明了两点法解的存在性和唯一性,并在这一结果的基础上设计出有效的算法。通过模拟计算可以看出,两点法与目前普遍使用的二阶矩法和点估计下限法相比,近似的精确性明显提高,尤其在小子样情形下效果更为显著。

Beta distribution approximation of confidence distributions and application in reliability statistics

In complex systems reliability assessment methodologies,using beta distributions to approximate all kinds of probability distributions on 0,1] is a common project methodology.Most work in application often uses second order moment method and point estimation and bounded below method.To reduce the approximation error,this paper conducts in-depth research on two point method proposed by the paper 1],and proves that its solution exists and is unique.Moreover,it gives effective algorithm on the basis of this result.Through simulation calculations we can see that its accuracy will be improved markedly compared with two others',and it is especially effective in case of small sample.