ThmDex – An index of mathematical definitions, results, and conjectures.
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▼ Zermelo-Fraenkel set theory
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▼ Random real number moment
Definition D2013
Random real number central moment
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}
Also known as
Centered moment
Children
▶ D2142: Random real number kurtosis
▶ D2141: Random real number skewness
Results
▶ R4595: Basic real calculus expression for moments of centred gaussian random basic real number
▶ R3547: Expectation minimises second central moment for random real number
▶ R4596: Real calculus expression for moments of standard gaussian random real number