序约束下三指数总体均值的极大似然估计

Maximum Likelihood Estimation of Ordered Means of Three Exponential Populations

令 Xi,i=1 ,2 ,3,为来自第 i个指数总体的观察值 ,其中均值 λi 均未知 ,但根据以往的经验 ,可以假定均值间满足一定的约束关系 ,如简单半序。本文给出了此种序约束下 λi 的极大似然估计λ*i ,并且证明了每一λ*i 比通常的估计 Xi

Let Xi,i =1,2,3 Be the observations from three exponential distributions with unknown means λ i .From experience,we may assume that there are some order restrictions among the means,for example,simple order restrictions.The maximum likelihood estimator λ  i is given in this paper,and it can be shown that λ  i has a smaller mean square error than that of the usual estimator X i ,for each i =1,2,3.