正态总体方差的最短区间估计与最佳双边检验

The Shortest Confidence Interval and the Best Two-Side Test of the Variance of a Normal Random Variable

用传统方法得到的正态总体的方差的置信区间显然不是最短的 ,因而在这个意义上说也不是最佳的 .对从 3到 45的 n及α=0 .2 5 ,0 .2 0 ,0 .1 5 ,0 .1 0 ,0 .0 5 ,0 .0 1 ,0 .0 0 5 ,我们得到了附表一 ,由此可以查出相应的最短置信区间 .同样 ,在对正态总体的方差进行双边检验时 ,传统的方法给出的临界值也不是最佳的 .对如下的 n和 α我们得到了附表二 ,由此可以查出最佳的临界值 .

The confidence interval of the variance of a normal random variable, obtained by using the traditional method of interval estimation, is obviously not the shortest one, in this sense it is not the best one. For n from 3 to 45 and for α =0 25, 0 20, 0 15, 0 10, 0 05, 0 01, 0 005, we have got Table 1 from which one can easily get the shortest confidence interval. When testing the two\|sided hypothesis on the variance of a normal random variable, the traditional choice of the boundary values is obviously not the best one. For the same values of n and α as above, we have worked out Table 2 that gives us the best choice of the boundary values in some sense. The programs carrying out all the needed computations are written by ourselves.