Kurtosis
Moors' interpretation

In 1986 Moors gave an interpretation of kurtosis. Let Z = X − μ σ, {\displaystyle Z={\frac {X-\mu }{\sigma }},} where X is a random variable, μ is the mean and σ is the standard deviation.

Now by definition of the kurtosis κ {\displaystyle \kappa }, and by the well-known identity E = var + ] 2, {\displaystyle E\left=\operatorname {var} +]^{2},} κ = E = var + ] 2 = var + ] 2 = var + 1. {\displaystyle \kappa =E\left=\operatorname {var} \left+\left\right]^{2}=\operatorname {var} \left+]^{2}=\operatorname {var} \left+1.}

The kurtosis can now be seen as a measure of the dispersion of Z around its expectation. Alternatively it can be seen to be a measure of the dispersion of Z around +1 and −1. κ attains its minimal value in a symmetric two-point distribution. In terms of the original variable X, the kurtosis is a measure of the dispersion of X around the two values μ ± σ.

High values of κ arise in two circumstances:
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