Random real number central moment

▾ 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

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

Child definitions

» D2142: Random real number kurtosis
» D2141: Random real number skewness

Results

» R3959: Affine coefficients which minimize expectation of squared distance from a target random real number

» R4594: Real calculus expression for central moments of gaussian random real number about expectation

» R4595: Basic real calculus expression for moments of centred gaussian random basic real number

» R4596: Real calculus expression for moments of standard gaussian random real number

» R3547: Expectation minimises second central moment for random real number

» R5466: Linear slope which minimizes expectation of squared distance from a target random real number