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