| layout |
mathjax |
author |
affiliation |
e_mail |
date |
title |
chapter |
section |
topic |
definition |
sources |
def_id |
shortcut |
username |
definition |
true |
Joram Soch |
BCCN Berlin |
joram.soch@bccn-berlin.de |
2020-10-07 20:47:00 -0700 |
Standardized moment |
General Theorems |
Probability theory |
Further moments |
Standardized moment |
| authors |
year |
title |
in |
pages |
url |
Wikipedia |
2020 |
Moment (mathematics) |
Wikipedia, the free encyclopedia |
retrieved on 2020-10-08 |
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D99 |
mom-stand |
JoramSoch |
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 $\sigma$:
$$ \label{eq:mom-stand}
\mu_n^{*} = \frac{\mu_n}{\sigma^n} = \frac{\mathrm{E}[(X-\mu)^n]}{\sigma^n} ; .
$$