Moment (probability)

Excess kurtosis

The excess kurtosis Kurt[𝑋] of a real random variable 𝑋 :𝜉 →ℝ with mean 𝜇 and variance 𝜎2 is a shifted version of the fourth standardized moment of 𝑋 prob

Kurt[𝑋]=𝔼⁡[(𝑋−𝜇𝜎)4]−3

where the unshifted version is sometimes referred to as the kurtosis (although this term is also used for the shifted version). The reason for the shift is that it ensures that any normal distribution has excess kurtosis of zero.

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