正态分布中期望与方差的最优联合置信区域

The optimal joint confidence region of expectation and variance of normal distribution

当总体为正态分布时,研究了其期望与方差参数的最优联合置信区域。一方面,我们得到了期望与方差联合置信区域的面积表达式;另一方面,在假设参数β1,β2之间存在倍数关系的情形下,得出当β1=1.02β2时的联合置信区域为最优的结论,且优于传统的当β1=β2时的联合置信区域。研究方法适用于β1和β2成非倍数关系的情形,也适用于研究其它分布中未知参数的最优联合置信区域。

In this paper,the optimal joint confidence region of expectation and variance parameters are studied when the population is a normal distribution.On the one hand,we get the area expression of the joint confidence region of expectation and variance.On the other hand,under the assumption that there is a multiple relationship between the parametersβ1 andβ2,it is concluded that the joint confidence region is optimal whenβ1=1.02β2,which is superior to the traditional joint confidence region whenβ1=β2.The method in this paper is suitable for the case whereβ1 andβ2 are non-multiples,and it is also suitable for the study of the optimal joint confidence region of unknown parameters in other distribution.