摘要
峰度通常被认为是衡量一个分布尾重的量,一些作者认为峰度是衡量分布在均值附近尖峰度的量。设已有总体样本x1,…,xn,样本峰度记为kn。关于样本均值x-对称地投入两个点xn+1,xn+2,得到新的样本x1,…,xn+2 相应的样本峰度记为kn+2。本文讨论了随着投入点xn+1,xn+2的位置不同,kn+2相对于kn的变化情况,并通过这种变化来探讨总体峰度的统计意义,认为峰度是总体离群数据离群度的度量。
Kurtosis is usually regarded as measure of heaviness of distribution tails. Some of writers describe the Kurtosis as ＂Pea- kness＂ of distribution. Given x1, …, xn, Sample Kurtosis is denoted by kn. We get the new sample x1,…,x（n-2） by increasing symmetrically two points according to x and denote the Sample Kurtosis of new data with k（n-2）.In this paper, the kinds of changing situations of k（n-2） according to kn with the different sites of increasing points x（n＋1） and x（n＋2）are presented. Statistical meanings of kurtosis is given： kurtosis is a kind of measure of data＇s degree of outlier.
出处
《燕山大学学报》
CAS
2006年第1期57-60,共4页
Journal of Yanshan University
关键词
峰度
JENSEN不等式
离群度
尾重
kurtosis
Jensen inequality
degree of outlier
heaviness of tails
