Wölbung einer reellwertigen Zufallsvariable

$$\begin{array}{rl}v(X)& =\frac{\text{4 te zentrale Moment}}{{\text{Standartabweichung}}^4}\\ & =\frac{{\mu }_4(X)}{SD(X{)}^4}=\frac{{\mu }_4(X)}{Var(X{)}^{\frac{1}{2}}}=\frac{{\mu }_4(X)}{{\mu }_2(X{)}^{\frac{1}{2}}}\\ & \text{oder}\\ & =\mathbb{E}[X^4]\left(\frac{X-\mathbb{E}[X]}{SD(X)}\right)\end{array}$$

Exess Kurtosis

$\mathbb{E}[X^4]\left(\frac{X-\mathbb{E}[X]}{SD(X)}\right)-3$