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Factorial moment
In probability theory, the nth factorial moment of a probability distribution, also called the nth factorial moment of any random variable X with that probability distribution, is
- E((X)n)
where
is the falling factorial (confusingly, this same notation, the Pochhammer symbol (x)n, is used by some mathematicians, especially in the theory of special functions, to denote the rising factorial x(x + 1)(x + 2) ... (x + n − 1); the present notation is used by combinatorialists).
For example, if X has a Poisson distribution with expected value λ, then the nth factorial moment of X is
- E((X)n) = λn.
See also moment (mathematics), cumulant.
Last updated: 10-17-2005 09:02:16
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details