Visualizing Peak and Tails to Introduce Kurtosis
Visualizing Peak and Tails to Introduce Kurtosis
复制标题
DOI：
10.1198/000313008x364516
复制
发表时间：
2008-11-01
影响因子：
1.8
通讯作者：
Seier, Edith
中科院分区：
文献类型：
--
作者：
Kotz, Samuel;Seier, Edith
本文提出了一种有限方差连续分布的峰尾可视化的简单方法。通过将所考虑的分布与等中心、等变异性的均匀分布进行比较，识别出单峰对称分布和非对称分布中的多余峰尾区，以及U型分布中的缺失区。对于所考察的分布，发现与基于CDF的峰度排序一致，并且总峰面积和尾部面积与分位数峰度之间具有很强的相关性。尾部和峰部的可视化可以用来在本科统计学课程中引入峰度的概念。
This article proposes a simple method to visualize peak and tails in continuous distributions with finite variance. The excess peak and tails areas in unimodal symmetric and nonsymmetric distributions, and the missing area in U-shaped distributions, are identified by comparing the distribution under consideration with the uniform distribution with equal center and variability. Agreement with kurtosis orderings based on the CDFs, and a strong correlation between the total peak and tails area with quantile kurtosis, were found for the distributions examined. The visualization of tails and peak could be used to introduce the notion of kurtosis in undergraduate statistics courses.