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

作　　者：熊明[1] 谢民育[1] 

机构地区：[1]华中师范大学数学与统计学学院,武汉430079

出　　处：《数学物理学报（A辑）》2009年第3期685-690,共6页Acta Mathematica Scientia

基　　金：国家自然科学基金(10571070)资助

摘　　要：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.

关 键 词：均值混合正态分布 方差混合正态分布 平移不变量 刻度不变量 稳健性 

分 类 号：O212.1[理学—概率论与数理统计]