Factorial moment generating function: Difference between revisions

Revision as of 16:08, 2 October 2006

Revision as of 02:34, 11 October 2006

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

::<math>E\left((X)_n\right)=M_X^{(n)}(1)=\left.\frac{\mathrm{d}^n}{\mathrm{d}t^n}\right|_{t=1} M_X(t),</math>

where the [[Pochhammer symbol]] (''x'')_''n'' is the [[falling factorial]]