摘要
在相关文献工作的基础上完善指数抽样分布定理.首先导出指数分布样本最大值与样本最小值之差的分布,并证明了样本最大值与样本最小值之差和样本最小值相互独立;然后导出指数分布样本最大值与样本均值之差的分布,并证明了样本最大值与样本均值之差和样本最小值相互独立.从而构造出三个期望之极小方差无偏估计,基于样本均值与样本最小值之差和样本最小值构造出的期望之极小方差无偏估计,恰好是期望之一致最小方差无偏估计;文末,在小样本情景下,对上述三个期望之极小方差无偏估计作了有效性比较.
This article continues the works of references, so as to improve and perfect the exponential sample theorem.first, the distribution of the difference between sample maximum and minimum of exponential distribu- tion is derived,and that the difference of these two statistics is mutually independent with the sample minimum is proven. Also, this article derives the distribution of the difference between sample maximum and sample mean, and demonstrates that the difference of these two statistics is mutually independent with the sample minimum. Thus, the three locM minimum variance unbiased estimators could be built,the one which is built by sample minimum and the difference between sample mean and sample minimum, is precisely the UMVUE of of mean of the Exponential distribution. At last, in small sample, the efficiency comparison is made among above-mentioned three local minimum variance unbiased estimators of mean of the Exponential distribution.
出处
《纯粹数学与应用数学》
2017年第6期568-577,共10页
Pure and Applied Mathematics
基金
宁波大学学科项目(XKL14D2037)
关键词
指数抽样分布定理
样本最大值
差
分布
期望
极小方差无偏估计
有效性
exponential sample theorem, sample maximum, difference, distribution, mean, local minimum variance unbiased estimator, efficiency
