Definition: Standardized moment
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The Book of Statistical Proofs ▷
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Standardized moment
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Metadata: ID: D99 | shortcut: mom-stand | author: JoramSoch | date: 2020-10-08, 03:47.
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 $\sigma$:
\[\label{eq:mom-stand} \mu_n^{*} = \frac{\mu_n}{\sigma^n} = \frac{\mathrm{E}[(X-\mu)^n]}{\sigma^n} \; .\]- Wikipedia (2020): "Moment (mathematics)"; in: Wikipedia, the free encyclopedia, retrieved on 2020-10-08; URL: https://en.wikipedia.org/wiki/Moment_(mathematics)#Standardized_moments.
Metadata: ID: D99 | shortcut: mom-stand | author: JoramSoch | date: 2020-10-08, 03:47.