Kurtosis

The kurtosis of a sample X = {x1, x2, ..., xn}, is the fourth moment:

K(X) = ((x1 - μ)4 + (x2 - μ)4 + ... + (xn - μ)4)/σ4

where μ is the mean of the sample X, and σ is the standard deviation.

If the data X are normally distributed, then K(X) = 3.

If K(X) > 3, X has large deviations (large tails) and is more peaked.

If K(X) < 3, X has small tails and is less peaked.

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