Index: The Book of Statistical ProofsGeneral Theorems ▷ Probability theory ▷ Further moments ▷ Standardized moment

Definition: Let $X$ be a random variable with expected value $\mu$ and standard deviation $\sigma$ and let $n$ be a positive integer. Then, the $n$-th standardized moment of $X$ is defined as the $n$-th moment of $X$ about the value $\mu$, divided by the $n$-th power of $\sigma$:

\[\label{eq:mom-stand} \mu_n^{*} = \frac{\mu_n}{\sigma^n} = \frac{\mathrm{E}[(X-\mu)^n]}{\sigma^n} \; .\]

Metadata: ID: D99 | shortcut: mom-stand | author: JoramSoch | date: 2020-10-08, 03:47.