基于Bootstrap方法的小子样试验评估方法研究

Bootstrap方法是一种小子样试验评估方法。该方法在产生随机样本方面有不足之处,即产生的随机样本受到原始样本范围限制。因此本文在研究了用指数分布函数、Boltzm ann函数和三次多项式函数拟合修正样本经验分布函数的可行性之后,讨论用修正的样本经验分布函数替换传统Bootstrap方法中的经验分布函数,提出了基于Bootstrap方法的小子样试验评估方法。结论表明:采用Boltzm ann和三次多项式函数拟合修正样本经验分布函数后可使产生的随机样本不受原始样本范围限制,提高试验评估结果的精度,并附有算例说明所提出的方法。

Study on Small Scale Sample Test Estimation Method Based on Bootstrap Method

The objective of this paper is to present a method that can be used to improve the conventional Bootstrap method.In the past,the Bootstrap method was for estimating small sample tests.Firstly,we point out the shortcomings of the Bootstrap method that Bootstrap random samples are confined to original samples.In particular,the maximum value and the minimum value of these random samples are limited in number.In order to solve the problem,we propose that exponential function be used to substitute the empirical cumulative distribution function(CDF) of the conventional Bootstrap method.Secondly the feasibility of the exponential function,Boltzmann function and three-cubed polynomial function modified by sample empirical CDF is studied.We conclude that the above problem can be solved by useing Boltzmann function and three-cubed polynomial function modified by sample empirical CDF so that the precision of estimation can be improved.Lastly,some examples are presented to illustrate the application of small scale sample test estimation method on the basis of the conventional Bootstrap method presented in the paper.