正态总体均值与标准差比在简单半序约束下的最大似然估计

Maximum Likelihood Estimation of Ratios of Means and Standard Deviations from Normal Populations with Different Sample Numbers under Semi-Order Restriction

中文关键词:  简单半序  最大似然估计  似然函数  PAVA算法.

英文关键词:semi-order restriction  maximum likelihood estimator  likelihood function  PAVA algorithm.

中文摘要:

      本文考虑两个正态总体均值和方差是未知参数,均值与标准差的比在简单半序约束下,且样本个数不同时,计算均值和标准差的最大似然估计的问题.给出了计算均值和标准差的最大似然估计的方法.同时还给出了三个总体均值与标准差的比在简单半序约束下求均值和标准差的最大似然估计的计算方法,并给出了迭代算法的模拟结果.

英文摘要:

      For two normal populations with unknown means $\mu_i $ and variances $\sigma_i^2>0$, $i=1,2$, assume that there is a semi-order restriction between ratios of means and standard deviations and sample numbers of two normal populations are different. A procedure of obtaining the maximum likelihood estimators of $\mu_i$'s and $\sigma_i$'s under the semi-order restrictions is proposed. For $i=3$ case, some connected results and simulations are given.