正态总体均值与标准差比在半序约束下的最大似然估计(英文)

Maximum Likelihood Estimation of Ratios of Means and Standard Deviations from Normal Populations under Semi-order Restriction

考虑两个正态总体X_i～N(μ_i,σ_i^2) i=1,2,均值μ_i和方差σ_i^2>0是未知参数,它们的比在半序约束μ_1/σ_1≤μ_2/σ_2下的最大似然估计(MLE)问题,给出了计算MLE的方法,对三个正态总体的情况,给出了相关的结果,这些方法在生物遗传和药物检验等方面都有广泛应用。

For two normal populations with unknown means ui and variances (ri2 > 0, i = 1 , 2. Assume that there is a semi-order restriction between ratios of means and standard deviations. A procedure of obtaining the maximum likelihood estimators of and under the semi-order restrictions is proposed. For i = 3 case, some connected results are given. These methods are abroad applied in biologic -al inheritance and medicinal test.