ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Deduction system
Zermelo-Fraenkel set theory
Binary cartesian set product
Binary relation
Simple map
Simple function
Measurable simple complex function
Simple integral
Unsigned basic integral
Unsigned basic expectation
Basic expectation
Random real number moment
Random real number central moment
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}