两个未知均值方差混合模型有限制下对数极大似然比的极限分布(英文)

The Limit Distribution of the Restricted Log Maximum Likelihood Ratio for Mixture Models of Two Normal Distributions with Unknown Mean and Variance

本文讨论了检验样本是来自一个正态总体还是两个未知均值和方差的正态的混合分布，采用对数极大似然比的检验．如果不加限制，Ｈａｒｔｉｎｇａｎ曾指出不是寻常的Ｘ２分布．我们在混合的权加了一点限制后得到了其极限分布并给出了分位点数值表．

The limit distribution of the log maximum likelihood ratio statistic for finite mixture models is not the usual chisqure (Hartigan 1985). We have considered the limit distribution of the restricted log maximum likehood ratio for mixture models of two distributions with single unknown parameter [2]. But it does not contain mixture models of two useful normal distribution with unknown mean and variance, it has another limit distribution. In this papaer, we give this limit distribution and its tables of values.