Definition:Standardized Moment
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Definition
Let $X$ be a random variable on some probability space with standard deviation $\sigma$.
Then the $n$th standardized moment of $X$, usually denoted $\alpha_n$, is defined as:
- $\alpha_n = \dfrac {\mu_n} {\sigma^n}$
where $\mu_n$ is the $n$th central moment of $X$.
The third standardized moment of $X$ is the skewness of $X$, and is usually denoted $\gamma_1$.
The fourth standardized moment of $X$ is the kurtosis of $X$, and is usually denoted $\alpha_4$.
Also see
Sources
- Weisstein, Eric W. "Standardized Moment." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/StandardizedMoment.html