Bayes Bootstrap改进方法
A Improvement Method of Bayes Bootstrap

小样本情况下实验数据的分布较难确定，工程上常采用Bootstrap和Bayes Bootstrap方法。在现有的文献中，该方法对小样本可靠性参数估计仅仅是重复利用原样本信息，通过扩大样本容量进行参数估计。在样本量较小的情况下，再生样本极易淹没原生样本信息导致估计偏差。本文在原方法的基础上，提出对Bayes Bootstrap方法的改进意见，在抽样过程中增加样本容量并通过对最大(最小)次序统计量领域进行扩充而达到对原始样本扩充的目的，最后用指数分布修正经验分布函数，以提高估计的精度。实验结果表明，改进后的Bayes Bootstrap方法对精度的估计有所提高，比原方法效果更好。
It is difficult to determine the distribution of experimental data under the condition of small samples. Bootstrap and Bayes Bootstrap methods are often used in engineering. In the existing literature, this method only reuses the original sample information to estimate the reliability parameters of small samples by expanding the sample size. When the sample size is small, it is easy for the regenerated sample to drown the original sample information, resulting in the estimation deviation. On the basis of the original method, this paper proposes suggestions on improving Bayes Bootstrap. In the sampling process, the sample size is increased, and the purpose of expanding the original sample is achieved by expanding the maximum (minimum) order statistics. Finally, the empirical distribution function is modified by exponential distribution to improve the estimation accuracy. The experimental results show that the improved Bayes Bootstrap method has better accuracy estimation than the original method.