正态总体方差最短置信区间的研究

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

从置信区间的本质意义出发,通过数值计算的方法,对于给定的置信度γ=0.90,0.95和0.99,在样本容量n从3到30的范围内,在正态总体均值未知的情形下,求得了方差σ2的最短置信区间,并对用通常方法求得的置信区间的长度与最短置信区间的长度进行了对比分析。结果表明,在小样本的情形下,用最短置信区间来作未知方差σ2的区间估计,将会使估计精度得到显著的提高。

Based on the definition of the confidence interval, using the methed of numerical calculation, the minimum length of confidence interval for the variance of the normal distribution are found. The sample sizes from 3 to 30 and confidence coeficients (γ= 0.90 , 0. 95 and 0. 99) are considered. Two kinds of confidence interval length, computed by the general method and by the method in the paper, are compared and analyzed. When sample size is not large, result shows that the precision of the interval estimaton about the variance of the normal distribution is remarkably increased.