On the meaning and use of kurtosis
On the meaning and use of kurtosis
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DOI：
10.1037/1082-989x.2.3.292
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发表时间：
1997-09-01
影响因子：
7
通讯作者：
DeCarlo, LT
中科院分区：
文献类型：
--
作者：
DeCarlo, LT
对于对称单峰分布，正峰度表示相对于正态分布的重尾和峰性，而负峰度表示轻尾和平坦。然而，许多教科书对峰度的描述或说明不完整或不正确。在本文中，峰度用众所周知的分布来说明，并讨论了其解释和误解的各个方面。峰度在检验单变量和多变量正态性中的作用，作为偏离正态的度量；在鲁棒性、异常值和双峰性问题上；在广义检验和估计中，讨论了峰度度量beta(2)的局限性和替代方法。
For symmetric unimodal distributions, positive kurtosis indicates heavy tails and peakedness relative to the normal distribution, whereas negative kurtosis indicates light tails and flatness. Many textbooks, however, describe or illustrate kurtosis incompletely or incorrectly. In this article, kurtosis is illustrated with well-known distributions, and aspects of its interpretation and misinterpretation are discussed. The role of kurtosis in testing univariate and multivariate normality, as a measure of departures from normality; in issues of robustness, outliers, and bimodality; in generalized tests and estimators, as well as limitations of and alternatives to the kurtosis measure beta(2), are discussed.