Definition:Moment Generating Function

Definition

Let $X$ be a random variable.

Then the moment generating function of $X$ is defined and denoted as:

$\map {M_X} t = \expect {e^{t X} }$

for all $t$ such that this expectation exists.

Also known as

The term moment generating function is commonly abbreviated to MGF or M.G.F.

Also see

• Results about moment generating functions can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): moment generating function
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): moment generating function
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): moment generating function