正态总体方差最短置信区间的估计  

Study on Minimum Length of Confidence Interval for Variance of Normal Distriblltions

作　　者：李生彪[1] 彭建奎[1] 

机构地区：[1]兰州文理学院,甘肃兰州730000

出　　处：《兰州文理学院学报（自然科学版）》2014年第4期6-9,共4页Journal of Lanzhou University of Arts and Science(Natural Sciences)

基　　金：甘肃省高等学校科研项目(2013A-135)

摘　　要：用传统对称方法得到的正态总体方差的置信区间显然不是最短的,因而从精确度这个意义上说也不是最佳的.从置信区间的定义出发,运用数值计算的方法,对于给定的置信度1-α=0.90,0.95和0.99,在样本容量n从6到35的范围内,求得了方差σ2的最短置信区间,并与用传统对称方法求得的置信区间与最短置信区间的长度进行了对比研究.结果表明,在样本容量n较小情形下,用最短置信区间来作方差σ2的区间估计,将会显著提高估计的精确度.Using the traditional method of interval estimation,to be obtained the confidence interval of nomal distribution variance is obviously not the shortest one,in this sense it is not the best one.Based on the definition of the confidence interval,using the method of numerical calculation,the minimum length of confidence interval for the variance of the normal distribution were found.The sample sizes from 6to 35 and confidence coefficients（1-α=0.90,0.95 and 0.99）are considered.Two kinds of confidence interval length are compared and analyzed.When sample size is not large,result showed that the precision of the interval estimation is increased remarkably.

关 键 词：正态总体 方差 置信区间 最短 

分 类 号：O212[理学—概率论与数理统计]