Sample Kurtosis
For a sample of n values the sample excess kurtosis is
where m4 is the fourth sample moment about the mean, m2 is the second sample moment about the mean (that is, the sample variance), xi is the ith value, and is the sample mean.
The variance of the sample kurtosis of a sample of size n from the normal distribution is
An approximate alternative is 24/n but this is inaccurate for small samples.
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