两个正态总体均值在均值和标准差比等值条件下的似然比检验

A likelihood Ratio Test of Equality of Two Normal Population Means Under Condition of Equality of Proportions of Means and Standard Deviations

考虑两个正态总体的均值在均值和标准差比等值条件下的似然比检验问题。其中均值和方差是未知参数。给出了正态总体均值和标准差的最大似然估计 (ML E) 。

Considering two normal populations with unknown means μ\-i and unknown variances σ\+2\-i(i=1,2) a likelihood ratio test of equality of two normal population means under condition of equality of proportions of means and standard deviations of two normal populations is presented. The maximum likelihood estimators(MLE) of means and standard deviations and the asymptotic distribution of likelihood ratio statistic are given.