均值混合正态分布统计量的性质

数学物理学报 ›› 2009, Vol. 29 ›› Issue (3): 685-690.

均值混合正态分布统计量的性质

(华中师范大学数学与统计学学院 |武汉 430079)

收稿日期:2007-01-11 修回日期:2008-10-08 出版日期:2009-06-25 发布日期:2009-06-25
基金资助:
国家自然科学基金(10571070)资助

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

(School of Mathematics and Statistics, Huazhong Normal University, Wuhan 430079)

Received:2007-01-11 Revised:2008-10-08 Online:2009-06-25 Published:2009-06-25
Supported by:
国家自然科学基金(10571070)资助

摘要/Abstract

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.

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

Abstract:

Based on background in genetic analysis, this paper proposes a class of mean-mixture 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.

Key words: Mean-mixture of normal distribution, Variance-mixture of normal distribution, Translational transformation, Scaling transformation, Robust

中图分类号:

熊明, 谢民育. 均值混合正态分布统计量的性质[J]. 数学物理学报, 2009, 29(3): 685-690.

XIONG Ming, XIE Min-Yu. The Properties of Statistics of the Mean-mixture of Normal Distribution[J]. Acta mathematica scientia,Series A, 2009, 29(3): 685-690.