Definition:Raw Moment

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

• Definition:Moment (Probability Theory)
• Definition:Central Moment
• Definition:Standardized Moment

• 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