改进的Bootstrap方法对比及应用研究  

Comparative Study anel Application of Improved Bootstrap Method

作　　者：邹艳[1] 罗文强[1] 

机构地区：[1]中国地质大学(武汉)数理学院,湖北武汉430074

出　　处：《应用数学》2008年第S1期62-66,共5页Mathematica Applicata

基　　金：武汉市研究创新计划项目(20066002059)

摘　　要：本文针对小样本情形,在不改变原样本的情况下,对原样本的最大(最小)次序统计量进行领域上的扩充,以克服原来自助样本生成范围上的限制.这将在尽可能保持分布特性一致的情形下,大大降低其与原观测样本的相似性,同时也将数据分布的特性拓展至非观测点,它是一种近似,在尽可能少的偏离真实分布的前提下,实现了对真实分布的自助探索.本文针对样本量在10到30之间的时候所做的改进.最后,将改进的Bootstrap方法应用于工程可靠性指标的计算,从而检验方法的可行性.This paper does not change the circumstances in a small sample of the original sample,but uses the neighborhood expansion of the biggest and the smallest order statistics of the original sample to overcome the limitation of the scope of the original self-generated samples.This distribution is possible to maintain the same circumstances,greatly reducing its similarity with the original observation of the samples.Meanwhile,it also expands to the characteristics of non-observation data distribution.It can be seen as a kind of an approximation.At last,we get the exploration of the self-realization of the real distribution deviated from the true distribution as little as possible.And the improvements made in this paper is based on the sample size from 10 to 30.Finally,the method is used in project reliability analyses to improve the reliability of the method,and also test the feasibility.

关 键 词：BOOTSTRAP方法 可靠性指标 次序统计量 改进 

分 类 号：O213.2[理学—概率论与数理统计]