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.
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.
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.
本文提出从HNBUE分布类中检验指数分布的方法，证明检验统计量的渐近正态性和检验的相合性。
This paper proposes a test statistics for testing exponential distribution versus HNBUE, and proves the statistics approximate normal distribution and consistence.
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。
Under the normal distribution, the maximum likelihood estimator for the population parameter is proved to be unbiased and asymptotically normal.
证明估计的强相合性和渐近正态性，给出似然比检验统计量的极限分布，并讨论基于精确分布的检验问题。
The limit distributions of estimators and likelihood ratio test are given, the strong consistency of estimators is also proved.
并且证明了在正态分布的假设下，该总体平均因果效应的极大似然估计是相合无偏且渐近正态的。
The maximum likelihood estimator for population average treatment effect is proved to be consistent, unbiased and asymptotically normal.
并且证明了在正态分布的假设下，该总体平均因果效应的极大似然估计是相合无偏且渐近正态的。
The maximum likelihood estimator for population average treatment effect is proved to be consistent, unbiased and asymptotically normal.
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