Definition:Raw Moment
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Definition
Let $X$ be a random variable on some probability space.
Then the $n$th raw moment of $X$, usually denoted $\mu'_n$, is defined as:
- $\mu'_n = \expect {X^n}$
where $\expect X$ denotes the expectation of $X$.
That is, the $n$th raw moment of $X$ is its $n$th moment about $0$.
The first raw moment of $X$ is the mean of $X$, and is instead usually denoted $\mu$.
Also known as
Some sources refer to the raw moment of a random variable as its moment about the origin.
Also see
- Results about raw moments can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): moment
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): moment
- Weisstein, Eric W. "Moment." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Moment.html