Factorial moment generating function: Difference between revisions

Revision as of 21:46, 14 March 2006

Revision as of 21:47, 14 March 2006

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:<math>M_X(t)=E\left(t^{X}\right), \quad t \in \mathbb{R},</math>

wherever this expectation exists. The factorial moment generating function generates the [[factorial moment|factorial moments]]s of the [[probability distribution]].

Provided the factorial moment generating function exists in an interval around ''t''&nbsp;=&nbsp;1, the ''n''th moment is given by