moment generating function
Given a random variable , the moment generating function of is the following function:
for (if the expectation converges).
It can be shown that if the moment generating function of is defined on an interval around the origin, then
In other words, the th-derivative of the moment generating function evaluated at zero is the th moment of .
Title | moment generating function |
Canonical name | MomentGeneratingFunction |
Date of creation | 2013-03-22 11:53:51 |
Last modified on | 2013-03-22 11:53:51 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 10 |
Author | mathcam (2727) |
Entry type | Definition |
Classification | msc 60E05 |
Classification | msc 46L05 |
Classification | msc 82-00 |
Classification | msc 83-00 |
Classification | msc 81-00 |
Related topic | CharacteristicFunction2 |
Related topic | CumulantGeneratingFunction |