On a Class of Symmetric Nonnormal Distributions with a Kurtosis of Three
On a Class of Symmetric Nonnormal Distributions with a Kurtosis of Three
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关于一类峰度为 3 的对称非正态分布
DOI：
10.1007/978-1-4612-3990-1_6
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
G. Sebastian
中科院分区：
文献类型：
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作者：
B. Kale;G. Sebastian
众所周知，在皮尔逊系统中，正态分布是唯一由偏度为零和峰度为3的条件决定的。构造了一大类峰度为3的非正态对称分布。这里给出的分布可以在线性模型中用作正态误差的替代。然而，这类中的许多分布可能与正态分布在尾部和分布的中心部分有很大不同。此外，任何基于样本偏度和/或样本峰度的正态性检验对这些替代方案都具有零功率。
It is well known that within the Pearsonian system the normal distribution is uniquely determined by the condition that skewness is zero and kurtosis is 3. We construct a wide class of non-normal symmetric distributions with kurtosis equal to 3. The distributions presented here can be used in linear models as an alternative to the normal error. However, many distributions in this class can be very much different from the normal distribution in the tail as well as the central part of the distribution. Further, any test of normality based on sample skewness and/or sample kurtosis would have power zero against these alternatives.