给出了正态总体均值和标准差的最大似然估计（M LE），似然比检验统计量及其渐近分布等结果。

The maximum likelihood estimators(MLE) of means and standard deviations, and the asymptotic distribution of likelihood ratio statistic were given.

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因此得到了推广矩估计量的渐近分布，于是证明了推广估计量的渐近正态性。

Then we derive the asymptotical distribution of the extended moment estimator and prove its asymptotically normality.

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证明了此统计量是渐近正态的，并利用蒙特卡罗方法对统计量的渐进分布做了统计模拟。

It is proved that the statistics is asymptotic normality, and simulation of the statistics's asymptotic distribution is carried out with Monte Carlo method.

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