ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D2142
Random real number kurtosis
Formulation 2
Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number such that
(i) $p \in (0, \infty)$ is a D5407: Positive real number
(ii) \begin{equation} \mathbb{E} |X|^4 < \infty \end{equation}
The kurtosis of $X$ is the D993: Real number \begin{equation} \text{Kurt} X : = \mathbb{E} [ (X - \mathbb{E} X)^4 ] \end{equation}