Definition: Moment
Index: The Book of Statistical Proofs ▷ General Theorems ▷ Probability theory ▷ Further moments ▷ Moment
Sources:
Metadata: ID: D90  shortcut: mom  author: JoramSoch  date: 20200819, 05:24.
Definition: Let $X$ be a random variable, let $c$ be a constant and let $n$ be a positive integer. Then, the $n$th moment of $X$ about $c$ is defined as the expected value of the $n$th power of $X$ minus $c$:
\[\label{eq:mom} \mu_n(c) = \mathrm{E}[(Xc)^n] \; .\]The “$n$th moment of $X$” may also refer to:

the $n$th raw moment $\mu_n’ = \mu_n(0)$;

the $n$th central moment $\mu_n = \mu_n(\mu)$;

the $n$th standardized moment $\mu_n^{*} = \mu_n/\sigma^n$.
 Wikipedia (2020): "Moment (mathematics)"; in: Wikipedia, the free encyclopedia, retrieved on 20200819; URL: https://en.wikipedia.org/wiki/Moment_(mathematics)#Significance_of_the_moments.
Metadata: ID: D90  shortcut: mom  author: JoramSoch  date: 20200819, 05:24.