均值混合正态分布统计量的性质

The Properties of Statistics of the Mean-mixture of Normal Distribution

这篇文章基于基因遗传背景,提出了一类均值混合正态分布,它不同于通常所讨论的方差混合正态分布。作者研究了这类均值混合正态分布统计量的性质,给出了平移变换群下不变量的稳健性,即它与正态分布下该统计量有相同的性质,并且讨论了其它统计量的分布。

Based on background in genetic analysis, this paper proposes a class of meanmixture of normal distribution. It is different from the variance-mixture of normal distribution, which is discussed in several bibliographies in general. We principally consider the properties of statistics of the mean-mixture of normal distribution. It is shown that those statistics which are invariant under translational transformation are robust in the class of mean-mixture of normal distribution, that is, these statistics have the same properties as those of normal distribution. Then the mean-mixture of normal distribution has the advantage of easily transferring properties enjoyed by normal distribution. Besides, the distributions of several other statistics are discussed.