论文标题
二进制采样下极端分位数估计的顺序设计
A sequential design for extreme quantiles estimation under binary sampling
论文作者
论文摘要
我们提出了一种顺序设计方法，旨在基于与给定阈值相对应的二分法数据样本估算极端分位数。这项研究是出于物质可靠性的工业挑战的动机，包括估算出降低结果的试验中的故障分位数，即在测试的应力水平下样品是否失败。提出的解决方案是使用分裂方法的顺序设计，将目标概率水平分解为有条件的高阶事件概率的产物。该方法包括逐渐针对分布的尾部和在截短的分布下进行采样。该模型是GEV或Weibull，其参数的顺序估计涉及二进制数据的最大似然过程，这是由于与此类限制信息相关的较大不确定性。
We propose a sequential design method aiming at the estimation of an extreme quantile based on a sample of dichotomic data corresponding to peaks over a given threshold. This study is motivated by an industrial challenge in material reliability and consists in estimating a failure quantile from trials whose outcomes are reduced to indicators of whether the specimen have failed at the tested stress levels. The solution proposed is a sequential design making use of a splitting approach, decomposing the target probability level into a product of probabilities of conditional events of higher order. The method consists in gradually targeting the tail of the distribution and sampling under truncated distributions. The model is GEV or Weibull, and sequential estimation of its parameters involves an improved maximum likelihood procedure for binary data, due to the large uncertainty associated with such a restricted information.
