Definition: Moment

Index: The Book of Statistical Proofs ▷ General Theorems ▷ Probability theory ▷ Further moments ▷ Moment

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 $c$:

\[\label{eq:mom} \mu_n(c) = \mathrm{E}[(X-c)^n] \; .\]

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 $\mu_n^{*} = \mu_n/\sigma^n$.

 

Sources:

• Wikipedia (2020): "Moment (mathematics)"; in: Wikipedia, the free encyclopedia, retrieved on 2020-08-19; URL: https://en.wikipedia.org/wiki/Moment_(mathematics)#Significance_of_the_moments.

Metadata: ID: D90 | shortcut: mom | author: JoramSoch | date: 2020-08-19, 05:24.