ThmDex – An index of mathematical definitions, results, and conjectures.
F11969
Formulation 1
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|^p < \infty \end{equation}
The central moment of $X$ with respect to $p$ and $\lambda \in \mathbb{R}$ is the D993: Real number \begin{equation} \mathbb{E} \left[ (X - \lambda)^p \right] \end{equation}