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1·The maximum likelihood estimators(MLE) of means and standard deviations and the asymptotic distribution of likelihood ratio statistic are given.

根据截尾均值、平尾均值的定义和截尾正态分布，本文得到了这两种均值都是最或然估计量。

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

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。

3·In this paper, the asymptotic distribution and the asymptotic probability of the selected model by using the information criteria AIC are obtained.

在本文中，我们对从信息论准则AIC选择出的模型给出了渐近分布和渐近概率。

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

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。

5·Methods In this paper, the authors provided the asymptotic distribution about the statistic in the formulas by using the theories of distribution and the methods of approximative calculation.

方法 运用统计量的分布理论和近似计算方法 ，求出公式中所涉及统计量的渐近分布。

6·It is shown that, under both the null and the local alternatives, the random weighting statistics have the same asymptotic distribution as the original test statistic under the null hypotheses.

我们证明了在原假设和局部对立假设之下随机加权统计量的条件渐近分布与检验统计量在原假设之下的渐近分布相同。

7·It is shown that the asymptotic null distribution of the modified likelihood ratio test proposed is derived and found to be relatively simple and easily applied.

最新的文献表明这个提出的修正似然比检验统计量在零假设下的渐近分布是比较简单，并且是容易应用的。

8·The likelihood ratio criterion of sphericity test, its asymptotic expansion and limiting distribution are obtained.

论文得到了球形检验的似然比准则，它的渐近展开与极限分布。

9·Furthermore, the renewal equation and asymptotic formula of the distribution of the amount of the claim causing ruin are obtained.

此外，还得到了导致破产的索赔额的分布满足的瑕疵更新方程和渐近解。

10·We present several theorems on the distribution of prime powers. These results play a very important role in providing explicit bounds for the asymptotic existence theorems of RBIBD and PMD.

利用解析数论工具证明了算术级数数列中素数幂分布的若干结果，这些结果在提供RBIBD设计与PMD设计的渐近存在性定理的精确定界时具有重要作用。